{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T09:06:57Z","timestamp":1777540017968,"version":"3.51.4"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,12,23]],"date-time":"2023-12-23T00:00:00Z","timestamp":1703289600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,23]],"date-time":"2023-12-23T00:00:00Z","timestamp":1703289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s00373-023-02733-w","type":"journal-article","created":{"date-parts":[[2023,12,23]],"date-time":"2023-12-23T08:02:16Z","timestamp":1703318536000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Weak-Dynamic Coloring of Graphs Beyond-Planarity"],"prefix":"10.1007","volume":"40","author":[{"given":"Weichan","family":"Liu","sequence":"first","affiliation":[]},{"given":"Guiying","family":"Yan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,23]]},"reference":[{"key":"2733_CR1","unstructured":"Accurso, C., Chernyshov, V., Hand, L., Jahanbekam, S., Wenger. P.: Weak dynamic coloring of planar graphs. arXiv:1802.05953"},{"key":"2733_CR2","doi-asserted-by":"crossref","unstructured":"Angelini, P., Bekos, M.A., Kaufmann, M., Schneck, T.: Efficient generation of different topological representations of graphs beyond-planarity. In: Toth, C.D., Archambault, D. (eds.) Proceedings of 27th International Symposium on Graph Drawing (GD 2019) (2019)","DOI":"10.1007\/978-3-030-35802-0_20"},{"issue":"1","key":"2733_CR3","doi-asserted-by":"publisher","first-page":"23","DOI":"10.7155\/jgaa.00457","volume":"22","author":"MJ Bannister","year":"2018","unstructured":"Bannister, M.J., Cabello, S., Eppstein, D.: Parameterized complexity of 1-planarity. J. Graph Algorithms Appl. 22(1), 23\u201349 (2018)","journal-title":"J. Graph Algorithms Appl."},{"issue":"4","key":"2733_CR4","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1002\/jgt.3190190406","volume":"19","author":"O Borodin","year":"1995","unstructured":"Borodin, O.: A new proof of the 6 color theorem. J. Graph Theory 19(4), 507\u2013521 (1995)","journal-title":"J. Graph Theory"},{"issue":"41","key":"2733_CR5","first-page":"12","volume":"108","author":"OV Borodin","year":"1984","unstructured":"Borodin, O.V.: Solution of the ringel problem on vertex-face coloring of planar graphs and coloring of 1-planar graphs. Metody Diskretnogo Analiza 108(41), 12\u201326 (1984)","journal-title":"Metody Diskretnogo Analiza"},{"key":"2733_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.tcs.2016.04.026","volume":"636","author":"FJ Brandenburg","year":"2016","unstructured":"Brandenburg, F.J., Didimo, W., Evans, W.S., Kindermann, P., Liotta, G., Montecchiani, F.: Recognizing and drawing IC-planar graphs. Theor. Comput. Sci. 636, 1\u201316 (2016)","journal-title":"Theor. Comput. Sci."},{"issue":"5","key":"2733_CR7","doi-asserted-by":"publisher","first-page":"1803","DOI":"10.1137\/120872310","volume":"42","author":"S Cabello","year":"2013","unstructured":"Cabello, S., Mohar, B.: Adding one edge to planar graphs makes crossing number and 1-planarity hard. SIAM J. Comput. 42(5), 1803\u20131829 (2013)","journal-title":"SIAM J. Comput."},{"issue":"7\u20138","key":"2733_CR8","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.1016\/j.dam.2012.01.012","volume":"160","author":"Y Chen","year":"2012","unstructured":"Chen, Y., Fan, S., Lai, H.-J., Song, H., Sun, L.: On dynamic coloring for planar graphs and graphs of higher genus. Discrete Appl. Math. 160(7\u20138), 1064\u20131071 (2012)","journal-title":"Discrete Appl. Math."},{"key":"2733_CR9","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.dam.2022.06.003","volume":"321","author":"Y Chen","year":"2022","unstructured":"Chen, Y., Fan, S., Lai, H.-J., Xu, M.: Graph $$r$$-hued colorings\u2014a survey. Discrete Appl. Math. 321, 24\u201348 (2022)","journal-title":"Discrete Appl. Math."},{"key":"2733_CR10","volume-title":"Computers and Intractability. A Guide to the Theory of NP-Completeness","author":"MR Garey","year":"1990","unstructured":"Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., New York (1990)"},{"issue":"1","key":"2733_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00453-007-0010-x","volume":"49","author":"A Grigoriev","year":"2007","unstructured":"Grigoriev, A., Bodlaender, H.L.: Algorithms for graphs embeddable with few crossings per edge. Algorithmica 49(1), 1\u201311 (2007)","journal-title":"Algorithmica"},{"issue":"5","key":"2733_CR12","doi-asserted-by":"publisher","first-page":"7337","DOI":"10.3934\/math.2022409","volume":"7","author":"X Hu","year":"2022","unstructured":"Hu, X., Kong, J.: An improved upper bound for the dynamic list coloring of 1-planar graphs. AIMS Math. 7(5), 7337\u20137348 (2022)","journal-title":"AIMS Math."},{"key":"2733_CR13","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.dam.2016.01.016","volume":"206","author":"S Jahanbekam","year":"2016","unstructured":"Jahanbekam, S., Kim, J., Suil, O., West, D.: On r-dynamic coloring of graphs. Discrete Appl. Math. 206, 65\u201372 (2016)","journal-title":"Discrete Appl. Math."},{"issue":"3","key":"2733_CR14","doi-asserted-by":"publisher","first-page":"703","DOI":"10.7151\/dmgt.2397","volume":"43","author":"DV Karpov","year":"2023","unstructured":"Karpov, D.V.: An upper bound on the chromatic number of 2-planar graphs. Discuss. Math. Graph Theory 43(3), 703\u2013720 (2023)","journal-title":"Discuss. Math. Graph Theory"},{"issue":"13\u201314","key":"2733_CR15","doi-asserted-by":"publisher","first-page":"2207","DOI":"10.1016\/j.dam.2013.03.005","volume":"161","author":"S-J Kim","year":"2013","unstructured":"Kim, S.-J., Lee, S., Park, W.-J.: Dynamic coloring and list dynamic coloring of planar graphs. Discrete Appl. Math. 161(13\u201314), 2207\u20132212 (2013)","journal-title":"Discrete Appl. Math."},{"key":"2733_CR16","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.dam.2016.01.022","volume":"206","author":"Y Kim","year":"2016","unstructured":"Kim, Y., Lee, S., Oum, S.-I.: Dynamic coloring of graphs having no $$K_5$$ minor. Discrete Appl. Math. 206, 81\u201389 (2016)","journal-title":"Discrete Appl. Math."},{"key":"2733_CR17","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.cosrev.2017.06.002","volume":"25","author":"S Kobourov","year":"2017","unstructured":"Kobourov, S., Liotta, G., Montecchiani, F.: An annotated bibliography on 1-planarity. Comput. Sci. Rev. 25, 49\u201367 (2017)","journal-title":"Comput. Sci. Rev."},{"issue":"1\u20132","key":"2733_CR18","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1002\/jgt.21630","volume":"72","author":"VP Korzhik","year":"2013","unstructured":"Korzhik, V.P., Mohar, B.: Minimal obstructions for 1-immersions and hardness of 1-planarity testing. J. Graph Theory 72(1\u20132), 30\u201371 (2013)","journal-title":"J. Graph Theory"},{"issue":"1","key":"2733_CR19","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/0012-365X(95)00294-7","volume":"162","author":"A Kostochka","year":"1996","unstructured":"Kostochka, A., Stiebitz, M., Wirth, B.: The colour theorems of brooks and gallai extended. Discrete Math. 162(1), 299\u2013303 (1996)","journal-title":"Discrete Math."},{"issue":"3","key":"2733_CR20","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1002\/jgt.20448","volume":"64","author":"D Kr\u00e1l\u2019","year":"2010","unstructured":"Kr\u00e1l\u2019, D., Stacho, L.: Coloring plane graphs with independent crossings. J. Graph Theory 64(3), 184\u2013205 (2010)","journal-title":"J. Graph Theory"},{"issue":"16","key":"2733_CR21","doi-asserted-by":"publisher","first-page":"1997","DOI":"10.1016\/j.disc.2006.03.052","volume":"306","author":"H-J Lai","year":"2006","unstructured":"Lai, H.-J., Lin, J., Montgomery, B., Shui, T., Fan, S.: Conditional colorings of graphs. Discrete Math. 306(16), 1997\u20132004 (2006)","journal-title":"Discrete Math."},{"key":"2733_CR22","first-page":"193","volume":"68","author":"HPH-J Lai","year":"2003","unstructured":"Lai, H.P.H.-J., Montgomery, B.: Upper bounds of dynamic chromatic number. Ars Combin. 68, 193\u2013201 (2003)","journal-title":"Ars Combin."},{"key":"2733_CR23","unstructured":"Montgomery, B.: Dynamic coloring of graphs. PhD thesis, West Virginia University (2001)"},{"key":"2733_CR24","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/BF01215922","volume":"17","author":"J Pach","year":"1997","unstructured":"Pach, J., T\u00f3th, G.: Graphs drawn with few crossings per edge. Combinatorica 17, 427\u2013439 (1997)","journal-title":"Combinatorica"},{"issue":"1\u20132","key":"2733_CR25","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/BF02996313","volume":"29","author":"G Ringel","year":"1965","unstructured":"Ringel, G.: Ein sechsfarbenproblem auf der kugel. Abhandlungen aus dem Mathematischen Seminar der Universit\u00e4t Hamburg 29(1\u20132), 107\u2013117 (1965)","journal-title":"Abhandlungen aus dem Mathematischen Seminar der Universit\u00e4t Hamburg"},{"key":"2733_CR26","doi-asserted-by":"crossref","unstructured":"Schaefer, M.: Crossing numbers of graphs. Discrete Math. Appl. CRC Press, Boca Raton (2018)","DOI":"10.1201\/9781315152394"},{"key":"2733_CR27","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/j.ipl.2020.106083","volume":"169","author":"JC Urschel","year":"2021","unstructured":"Urschel, J.C., Wellens, J.: Testing gap $$k$$-planarity is NP-complete. Inf. Process. Lett. 169, 8 (2021). (Id\/No 106083)","journal-title":"Inf. Process. Lett."},{"issue":"12","key":"2733_CR28","doi-asserted-by":"publisher","first-page":"2045","DOI":"10.1007\/s10114-014-3763-6","volume":"30","author":"X Zhang","year":"2014","unstructured":"Zhang, X.: Drawing complete multipartite graphs on the plane with restrictions on crossings. Acta Math. Sin. Engl. Ser. 30(12), 2045\u20132053 (2014)","journal-title":"Acta Math. Sin. Engl. Ser."},{"key":"2733_CR29","doi-asserted-by":"crossref","unstructured":"Zhang, X., Li, Y.: Dynamic list coloring of 1-planar graphs. Discrete Math. 344(5), 8 (2021) (Id\/No 112333)","DOI":"10.1016\/j.disc.2021.112333"}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-023-02733-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-023-02733-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-023-02733-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,30]],"date-time":"2024-03-30T18:05:15Z","timestamp":1711821915000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-023-02733-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,23]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["2733"],"URL":"https:\/\/doi.org\/10.1007\/s00373-023-02733-w","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"value":"0911-0119","type":"print"},{"value":"1435-5914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,23]]},"assertion":[{"value":"18 October 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 November 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 November 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"7"}}