{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:05:02Z","timestamp":1740107102477,"version":"3.37.3"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,6,2]],"date-time":"2021-06-02T00:00:00Z","timestamp":1622592000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,6,2]],"date-time":"2021-06-02T00:00:00Z","timestamp":1622592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100005874","name":"Universit\u00e0 degli Studi G. D'Annunzio Chieti Pescara","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100005874","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The Maximum Weight Independent Set Problem (WIS) is a well-known NP-hard problem. A popular way to study WIS is to detect graph classes for which WIS can be solved in polynomial time, with particular reference to hereditary graph classes, i.e., defined by a hereditary graph property or equivalently by forbidding one or more induced subgraphs. Given two graphs <jats:italic>G<\/jats:italic> and <jats:italic>H<\/jats:italic>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$G+H$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>G<\/mml:mi>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:mi>H<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> denotes the disjoint union of <jats:italic>G<\/jats:italic> and <jats:italic>H<\/jats:italic>. This manuscript shows that (i) WIS can be solved for (<jats:inline-formula><jats:alternatives><jats:tex-math>$$P_4+P_4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msub>\n                      <mml:mi>P<\/mml:mi>\n                      <mml:mn>4<\/mml:mn>\n                    <\/mml:msub>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:msub>\n                      <mml:mi>P<\/mml:mi>\n                      <mml:mn>4<\/mml:mn>\n                    <\/mml:msub>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, Triangle)-free graphs in polynomial time, where a <jats:inline-formula><jats:alternatives><jats:tex-math>$$P_4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>P<\/mml:mi>\n                    <mml:mn>4<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is an induced path of four vertices and a Triangle is a cycle of three vertices, and that in particular it turns out that (ii) for every (<jats:inline-formula><jats:alternatives><jats:tex-math>$$P_4+P_4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msub>\n                      <mml:mi>P<\/mml:mi>\n                      <mml:mn>4<\/mml:mn>\n                    <\/mml:msub>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:msub>\n                      <mml:mi>P<\/mml:mi>\n                      <mml:mn>4<\/mml:mn>\n                    <\/mml:msub>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, Triangle)-free graph <jats:italic>G<\/jats:italic> there is a family <jats:inline-formula><jats:alternatives><jats:tex-math>$${{\\mathcal {S}}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>S<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of subsets of <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>) inducing (complete) bipartite subgraphs of <jats:italic>G<\/jats:italic>, which contains polynomially many members and can be computed in polynomial time, such that every maximal independent set of <jats:italic>G<\/jats:italic> is contained in some member of <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {S}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>S<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. These results seem to be harmonic with respect to other polynomial results for WIS on [subclasses of] certain <jats:inline-formula><jats:alternatives><jats:tex-math>$$S_{i,j,k}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>S<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mi>i<\/mml:mi>\n                      <mml:mo>,<\/mml:mo>\n                      <mml:mi>j<\/mml:mi>\n                      <mml:mo>,<\/mml:mo>\n                      <mml:mi>k<\/mml:mi>\n                    <\/mml:mrow>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-free graphs and to other structure results on [subclasses of] Triangle-free graphs.<\/jats:p>","DOI":"10.1007\/s00373-021-02340-7","type":"journal-article","created":{"date-parts":[[2021,6,2]],"date-time":"2021-06-02T19:08:35Z","timestamp":1622660915000},"page":"2173-2189","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Independent Sets in ($$P_4+P_4$$,Triangle)-Free Graphs"],"prefix":"10.1007","volume":"37","author":[{"given":"Raffaele","family":"Mosca","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,6,2]]},"reference":[{"key":"2340_CR1","volume-title":"Network Flows: Theory, Algorithms and Applications","author":"RK Ahuja","year":"1993","unstructured":"Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms and Applications. Prentice Hall, Englewood Cliffs (1993)"},{"key":"2340_CR2","first-page":"3","volume-title":"Combinatorial-Algebraic Methods in Applied Mathematics","author":"VE Alekseev","year":"1983","unstructured":"Alekseev, V.E.: On the local restrictions effect on the complexity of finding the graph independence number. In: Markov, A.A. (ed.), Combinatorial-Algebraic Methods in Applied Mathematics, pp. 3\u201313. Gorkiy University Press, Gorky (1983) (in Russian)"},{"key":"2340_CR3","first-page":"5","volume-title":"Combinatorial-Algebraic Methods in Applied Mathematics","author":"VE Alekseev","year":"1991","unstructured":"Alekseev, V.E.: On the number of maximal independence sets in graphs from hereditary classes. In: Shevchenko, V.N. (ed.), Combinatorial-Algebraic Methods in Applied Mathematics, pp. 5\u20138. Gorkiy University Press, Gorky (1991) (in Russian)"},{"key":"2340_CR4","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0166-218X(02)00290-1","volume":"135","author":"VE Alekseev","year":"2004","unstructured":"Alekseev, V.E.: A polynomial algorithm for finding largest independent sets in fork-free graphs. Discrete Appl. Math. 135, 3\u201316 (2004). (Discrete Analysis and Operations Research Ser. 1, 6 (1999) 3-19 (in Russian))","journal-title":"Discrete Appl. Math."},{"key":"2340_CR5","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/S0166-218X(03)00387-1","volume":"132","author":"VE Alekseev","year":"2004","unstructured":"Alekseev, V.E.: On easy and hard hereditary classes of graphs with respect to the independent set problem. Discrete Appl. Math. 132, 17\u201326 (2004)","journal-title":"Discrete Appl. Math."},{"key":"2340_CR6","doi-asserted-by":"crossref","unstructured":"Brandst\u00e4dt, A., Le, V.B., Spinrad, J.P.: Graph classes: a survey. In: SIAM Monographs on Discrete Math. Appl., Vol. 3. SIAM, Philadelphia (1999)","DOI":"10.1137\/1.9780898719796"},{"key":"2340_CR7","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/j.dam.2017.10.003","volume":"236","author":"A Brandst\u00e4dt","year":"2018","unstructured":"Brandst\u00e4dt, A., Mosca, R.: Maximum weight independent set for ($$P_7$$, Triangle)-free graphs in polynomial time. Discrete Appl. Math. 236, 57\u201365 (2018)","journal-title":"Discrete Appl. Math."},{"issue":"2018","key":"2340_CR8","first-page":"57","volume":"237","author":"A Brandst\u00e4dt","year":"2018","unstructured":"Brandst\u00e4dt, A., Mosca, R.: Maximum weight independent set for $$\\ell $$claw-free graphs in polynomial time. Discrete Appl. Math. 237(2018), 57\u201364 (2018)","journal-title":"Discrete Appl. Math."},{"key":"2340_CR9","unstructured":"Brandst\u00e4dt, A., Mosca, R.: Maximum weight independent sets for ($$S_{1,2,4}$$, Triangle)-free graphs in polynomial time. CoRR,abs\/1806.09472 (2018)"},{"key":"2340_CR10","doi-asserted-by":"publisher","first-page":"926","DOI":"10.1137\/0214065","volume":"14","author":"DG Corneil","year":"1985","unstructured":"Corneil, D.G., Perl, Y., Stewart, L.K.: A linear recognition algorithm for cographs. SIAM J. Comput. 14, 926\u2013934 (1985)","journal-title":"SIAM J. Comput."},{"key":"2340_CR11","unstructured":"De Crescenzo, L.: Storia della filosofia greca. Da Socrate in poi, Arnoldo Mondadori Editore, Milano (1986)"},{"key":"2340_CR12","unstructured":"Desler, J.F., Hakimi, S.L.: On finding a maximum stable set of a graph. In: Proc. 4th Annual Princeton Conf. on Information Science and Systems. Princeton, NJ (1970)"},{"key":"2340_CR13","doi-asserted-by":"crossref","unstructured":"Faenza, Y., Oriolo, G., Stauffer, G.: An algorithmic decomposition of claw-free graphs leading to an $$O(n^3)$$-algorithm for the weighted stable set problem. In: Randall, D. (ed.) Proceedings of the Twenty Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, San Francisco, California, USA, 23\u201325 January 2011, pp. 630\u2013646. SIAM (2011)","DOI":"10.1137\/1.9781611973082.49"},{"key":"2340_CR14","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/0012-365X(89)90268-9","volume":"73","author":"M Farber","year":"1989","unstructured":"Farber, M.: On diameters and radii of bridged graphs. Discrete Math. 73, 249\u2013260 (1989)","journal-title":"Discrete Math."},{"key":"2340_CR15","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1002\/net.3230230308","volume":"23","author":"M Farber","year":"1993","unstructured":"Farber, M., Hujter, M., Tuza, Zs.: An upper bound on the number of cliques in a graph. Networks 23, 75\u201383 (1993)","journal-title":"Networks"},{"key":"2340_CR16","first-page":"271","volume":"49","author":"GH Fricke","year":"1998","unstructured":"Fricke, G.H., Hedetniemi, S.T., Jacobs, D.P.: Independence and irredundance in $$k$$-regular graphs. Ars Combin. 49, 271\u2013279 (1998)","journal-title":"Ars Combin."},{"key":"2340_CR17","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0304-3975(76)90059-1","volume":"1","author":"MR Garey","year":"1976","unstructured":"Garey, M.R., Johnson, D.S., Stockmeyer, L.: Some simplified NP-complete graph problems. Theoret. Comput. Sci. 1, 237\u2013267 (1976)","journal-title":"Theoret. Comput. Sci."},{"key":"2340_CR18","doi-asserted-by":"publisher","first-page":"826","DOI":"10.1137\/0132071","volume":"32","author":"MR Garey","year":"1977","unstructured":"Garey, M.R., Johnson, D.S.: The rectilinear Steiner tree problem is NP-complete. SIAM J. Appl. Math. 32, 826\u2013834 (1977)","journal-title":"SIAM J. Appl. Math."},{"key":"2340_CR19","volume-title":"Computers and Intractability: A Guide to the Theory of NP-completeness","author":"MR Garey","year":"1979","unstructured":"Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco (1979)"},{"key":"2340_CR20","first-page":"325","volume":"21","author":"M Gr\u00f6tschel","year":"1984","unstructured":"Gr\u00f6tschel, M., Lov\u00e1sz, L., Schrijver, A.: Polynomial algorithms for perfect graphs. Ann. Discrete Math. 21, 325\u2013356 (1984)","journal-title":"Ann. Discrete Math."},{"key":"2340_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-97881-4","volume-title":"Geometric Algorithms and Combinatorial Optimization","author":"M Gr\u00f6tschel","year":"1988","unstructured":"Gr\u00f6tschel, M., Lov\u00e1sz, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer, Berlin (1988)"},{"key":"2340_CR22","doi-asserted-by":"crossref","unstructured":"Grzesik, A., Klimosova, T., Pilipczuk, M., Pilipczuk, M.: Polynomial-time algorithm for maximum weight independent set on P6-free graphs. In: Chan, T.M. (ed.) Proceedings of the 18 Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019, pp. 1257\u20131271. SIAM (2019)","DOI":"10.1137\/1.9781611975482.77"},{"issue":"2","key":"2340_CR23","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1137\/0406022","volume":"6","author":"M Hujter","year":"1993","unstructured":"Hujter, M., Tuza, Zs.: The number of maximal independent sets in triangle-free graphs. SIAM J. Discrete Math. 6(2), 284\u2013288 (1993)","journal-title":"SIAM J. Discrete Math."},{"key":"2340_CR24","doi-asserted-by":"publisher","unstructured":"Lokshantov, D., Vatshelle, M., Villanger, Y.: Independent set in $$P_5$$-free graphs in polynomial time. In: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, Oregon, USA, 5\u20137 January 2014, pp. 570\u2013581 (2014). https:\/\/doi.org\/10.1137\/1.9781611973402.43","DOI":"10.1137\/1.9781611973402.43"},{"key":"2340_CR25","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/j.dam.2016.04.012","volume":"231","author":"VV Lozin","year":"2017","unstructured":"Lozin, V.V.: From matchings to independent sets. Discrete Appl. Math. 231, 4\u201314 (2017)","journal-title":"Discrete Appl. Math."},{"key":"2340_CR26","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1016\/j.jda.2008.04.001","volume":"6","author":"VV Lozin","year":"2008","unstructured":"Lozin, V.V., Milani\u010d, M.: A polynomial algorithm to find an independent set of maximum weight in a fork-free graph. J. Discrete Algorithms 6, 595\u2013604 (2008)","journal-title":"J. Discrete Algorithms"},{"key":"2340_CR27","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.dam.2004.07.006","volume":"146","author":"VV Lozin","year":"2005","unstructured":"Lozin, V.V., Mosca, R.: Independent sets in extensions of $$2K_2$$-free graphs. Discrete Appl. Math. 146, 74\u201380 (2005)","journal-title":"Discrete Appl. Math."},{"key":"2340_CR28","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.tcs.2012.06.014","volume":"460","author":"VV Lozin","year":"2012","unstructured":"Lozin, V.V., Mosca, R.: Maximum regular subgraphs in $$2P_3$$-free graphs. Theoret. Comput. Sci. 460, 26\u201333 (2012)","journal-title":"Theoret. Comput. Sci."},{"key":"2340_CR29","doi-asserted-by":"publisher","first-page":"1449","DOI":"10.1016\/j.disc.2017.10.004","volume":"341","author":"F Maffray","year":"2018","unstructured":"Maffray, F., Pastor, L.: Maximum weight stable set in ($$P_7$$, bull)-free graphs and ($$S_{1,2,3}$$, bull)-free graphs. Discrete Math. 341, 1449\u20131458 (2018)","journal-title":"Discrete Math."},{"key":"2340_CR30","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1016\/0095-8956(80)90074-X","volume":"28","author":"GJ Minty","year":"1980","unstructured":"Minty, G.J.: On maximal independent sets of vertices in claw-free graphs. J. Combin. Theory Ser. B 28, 284\u2013304 (1980)","journal-title":"J. Combin. Theory Ser. B"},{"key":"2340_CR31","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/0166-218X(92)90041-8","volume":"35","author":"OJ Murphy","year":"1992","unstructured":"Murphy, O.J.: Computing independent sets in graphs with large girth. Discrete Appl. Math. 35, 167\u2013170 (1992)","journal-title":"Discrete Appl. Math."},{"key":"2340_CR32","first-page":"194","volume":"44","author":"D Nakamura","year":"2001","unstructured":"Nakamura, D., Tamura, A.: A revision of Minty's algorithm for finding a maximum weight stable set in a claw-free graph. J. Oper. Res. Soc. Jpn. 44, 194\u2013204 (2001)","journal-title":"J. Oper. Res. Soc. Jpn."},{"key":"2340_CR33","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/s10107-019-01461-5","volume":"186","author":"P Nobili","year":"2021","unstructured":"Nobili, P., Sassano, A.: An O($$n^2log(n)$$) algorithm for the weighted stable set problem in claw-free graphs. Math. Progr. 186, 409\u2013437 (2021)","journal-title":"Math. Progr."},{"key":"2340_CR34","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0020-0190(88)90143-3","volume":"28","author":"S Olariu","year":"1988","unstructured":"Olariu, S.: Paw-free graphs. Inf. Process. Lett. 28, 53\u201354 (1988)","journal-title":"Inf. Process. Lett."},{"key":"2340_CR35","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/0020-0190(90)90143-L","volume":"34","author":"S Olariu","year":"1990","unstructured":"Olariu, S.: On the closure of Triangle-free graphs under substitution. Inf. Process. Lett. 34, 97\u2013101 (1990)","journal-title":"Inf. Process. Lett."},{"key":"2340_CR36","doi-asserted-by":"crossref","unstructured":"Pilipczuk, M., Sintiari, N.L.D., Thomass\u00e9, S., Trotignon, N.: (Theta, triangle)-free and (even hole, K4)-free graphs. Part 2 : bounds on treewidth, CoRR,abs\/2001.01607 (2020)","DOI":"10.1002\/jgt.22675"},{"key":"2340_CR37","first-page":"307","volume":"15","author":"S Poljak","year":"1974","unstructured":"Poljak, S.: A note on stable sets and colorings of graphs. Commun. Math. Univ. Carol. 15, 307\u2013309 (1974)","journal-title":"Commun. Math. Univ. Carol."},{"key":"2340_CR38","unstructured":"Prisner, E.: Graphs with few cliques. In: Alavi, Y., Schwenk, A. (eds.) Proceedings of the 7th Quadrennial International Conference on Graph Theory, Algorithms, Combinatorics and Applications, pp. 945\u2013956. Western Michigam University, John Wiley and Sons, Inc. (1995)"},{"key":"2340_CR39","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1016\/S0012-365X(02)00511-3","volume":"257","author":"H-J Pr\u00f6mel","year":"2002","unstructured":"Pr\u00f6mel, H.-J., Schickinger, T., Steger, A.: A note on Triangle-free and bipartite graphs. Discrete Math. 257, 531\u2013540 (2002)","journal-title":"Discrete Math."},{"key":"2340_CR40","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0012-365X(90)90287-R","volume":"29","author":"N Sbihi","year":"1980","unstructured":"Sbihi, N.: Algorithme de recherche d'un independent de cardinalit\u00e9 maximum dans un graphe sans \u00e9toile. Discrete Math. 29, 53\u201376 (1980)","journal-title":"Discrete Math."},{"key":"2340_CR41","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1137\/0206036","volume":"6","author":"S Tsukiyama","year":"1977","unstructured":"Tsukiyama, S., Ide, M., Ariyoshi, H., Shirakawa, I.: A new algorithm for generating all maximal independent sets. SIAM J. Comput. 6, 505\u2013517 (1977)","journal-title":"SIAM J. Comput."}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-021-02340-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-021-02340-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-021-02340-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T21:27:30Z","timestamp":1636838850000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-021-02340-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,2]]},"references-count":41,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["2340"],"URL":"https:\/\/doi.org\/10.1007\/s00373-021-02340-7","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"type":"print","value":"0911-0119"},{"type":"electronic","value":"1435-5914"}],"subject":[],"published":{"date-parts":[[2021,6,2]]},"assertion":[{"value":"9 April 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 May 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}