{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T06:59:57Z","timestamp":1775717997796,"version":"3.50.1"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T00:00:00Z","timestamp":1772582400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T00:00:00Z","timestamp":1772582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"crossref","award":["NRF-2021K2A9A2A11101617"],"award-info":[{"award-number":["NRF-2021K2A9A2A11101617"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"crossref","award":["RS-2023-00211670"],"award-info":[{"award-number":["RS-2023-00211670"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12161141006"],"award-info":[{"award-number":["12161141006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010446","name":"Institute for Basic Science","doi-asserted-by":"publisher","award":["IBS-R029-C1"],"award-info":[{"award-number":["IBS-R029-C1"]}],"id":[{"id":"10.13039\/501100010446","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1007\/s00373-026-03031-x","type":"journal-article","created":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T15:32:15Z","timestamp":1772638335000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On a Variant of Dichromatic Number for Digraphs with Prescribed Sets of Arcs"],"prefix":"10.1007","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1820-1962","authenticated-orcid":false,"given":"O-joung","family":"Kwon","sequence":"first","affiliation":[]},{"given":"Xiaopan","family":"Lian","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,3,4]]},"reference":[{"issue":"3","key":"3031_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.37236\/6521","volume":"26","author":"P Aboulker","year":"2019","unstructured":"Aboulker, P., Cohen, N., Havet, F., Lochet, W., Moura, P.P., Thomass\u00e9, S.: Subdivisions in digraphs of large out-degree or large dichromatic number. Electron. J. Combin. 26(3), 3\u201319 (2019)","journal-title":"Electron. J. Combin."},{"issue":"1","key":"3031_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.37236\/10223","volume":"29","author":"P Aboulker","year":"2022","unstructured":"Aboulker, P., Havet, F., Knauer, K., Rambaud, C.: On the dichromatic number of surfaces. Electron. J. Combin. 29(1), 1\u201330 (2022)","journal-title":"Electron. J. Combin."},{"issue":"8","key":"3031_CR3","doi-asserted-by":"publisher","first-page":"883","DOI":"10.1006\/eujc.1997.0188","volume":"19","author":"B Bollob\u00e1s","year":"1998","unstructured":"Bollob\u00e1s, B., Thomason, A.: Proof of a conjecture of mader, erd\u0151s and hajnal on topological complete subgraphs. European J. Combin. 19(8), 883\u2013887 (1998)","journal-title":"European J. Combin."},{"issue":"4","key":"3031_CR4","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1145\/2700209","volume":"11","author":"R Chitnis","year":"2015","unstructured":"Chitnis, R., Cygan, M., Hajiaghayi, M., Marx, D.: Directed subset feedback vertex set is fixed-parameter tractable. ACM Trans. Algorithms 11(4), 28 (2015)","journal-title":"ACM Trans. Algorithms"},{"issue":"1","key":"3031_CR5","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1137\/110843071","volume":"27","author":"M Cygan","year":"2013","unstructured":"Cygan, M., Pilipczuk, M., Pilipczuk, M., Wojtaszczyk, J.O.: Subset feedback vertex set is fixed-parameter tractable. SIAM J. Discret. Math. 27(1), 290\u2013309 (2013)","journal-title":"SIAM J. Discret. Math."},{"issue":"4","key":"3031_CR6","doi-asserted-by":"publisher","first-page":"1231","DOI":"10.1137\/S0097539798340047","volume":"30","author":"G Even","year":"2000","unstructured":"Even, G., Naor, J., Zosin, L.: An 8-approximation algorithm for the subset feedback vertex set problem. SIAM J. Comput. 30(4), 1231\u20131252 (2000)","journal-title":"SIAM J. Comput."},{"key":"3031_CR7","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1016\/j.jctb.2020.09.006","volume":"146","author":"A Gir\u00e3o","year":"2021","unstructured":"Gir\u00e3o, A., Popielarz, K., Snyder, R.: Subdivisions of digraphs in tournaments. J. Combin. Theory Ser. B 146, 266\u2013285 (2021)","journal-title":"J. Combin. Theory Ser. B"},{"issue":"C","key":"3031_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jctb.2021.10.002","volume":"153","author":"L Gishboliner","year":"2022","unstructured":"Gishboliner, L., Steiner, R., Szab\u00f3, T.: Dichromatic number and forced subdivisions. J. Combin. Theory Ser. B 153(C), 1\u201330 (2022)","journal-title":"J. Combin. Theory Ser. B"},{"key":"3031_CR9","doi-asserted-by":"crossref","unstructured":"Gollin, J.P., Hendrey, K., Kawarabayashi, K.I., Kwon, O., Oum, S.: A unified half-integral erd\u0151s-p\u00f3sa theorem for cycles in graphs labelled by multiple abelian groups. J. Lond. Math. Soc. 109(1), e12858 (2024)","DOI":"10.1112\/jlms.12858"},{"issue":"2","key":"3031_CR10","doi-asserted-by":"publisher","first-page":"2507","DOI":"10.1007\/s00208-025-03293-5","volume":"393","author":"JP Gollin","year":"2025","unstructured":"Gollin, J.P., Hendrey, K., Kwon, O., Oum, S., Yoo, Y.: A unified erd\u0151s-p\u00f3sa theorem for cycles in graphs labelled by multiple abelian groups. Math. Ann. 393(2), 2507\u20132559 (2025)","journal-title":"Math. Ann."},{"issue":"1","key":"3031_CR11","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s00224-017-9805-6","volume":"62","author":"EC Hols","year":"2018","unstructured":"Hols, E.C., Kratsch, S.: A randomized polynomial kernel for subset feedback vertex set. Theory Comput. Syst. 62(1), 63\u201392 (2018)","journal-title":"Theory Comput. Syst."},{"issue":"1","key":"3031_CR12","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s00493-017-3683-z","volume":"39","author":"T Huynh","year":"2019","unstructured":"Huynh, T., Joos, F., Wollan, P.: A unified erd\u0151s-p\u00f3sa theorem for constrained cycles. Combinatorica 39(1), 91\u2013133 (2019)","journal-title":"Combinatorica"},{"issue":"2","key":"3031_CR13","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.aam.2012.03.002","volume":"49","author":"N Kakimura","year":"2012","unstructured":"Kakimura, N., Kawarabayashi, K.: Packing cycles through prescribed vertices under modularity constraints. Adv. in Appl. Math. 49(2), 97\u2013110 (2012)","journal-title":"Adv. in Appl. Math."},{"issue":"1","key":"3031_CR14","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1017\/S096354830000184X","volume":"5","author":"J Koml\u00f3s","year":"1996","unstructured":"Koml\u00f3s, J., Szemer\u00e9di, E.: Topological cliques in graphs. II. Combin. Probab. Comput. 5(1), 79\u201390 (1996)","journal-title":"II. Combin. Probab. Comput."},{"issue":"4","key":"3031_CR15","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1002\/jgt.22844","volume":"101","author":"T M\u00e9sz\u00e1ros","year":"2022","unstructured":"M\u00e9sz\u00e1ros, T., Steiner, R.: Complete directed minors and chromatic number. J. Graph Theory 101(4), 623\u2013632 (2022)","journal-title":"J. Graph Theory"},{"key":"3031_CR16","doi-asserted-by":"publisher","first-page":"E32","DOI":"10.1017\/fms.2016.28","volume":"4","author":"B Mohar","year":"2016","unstructured":"Mohar, B., Wu, H.: Dichromatic number and fractional chromatic number. Forum of Mathematics, Sigma 4, E32 (2016). https:\/\/doi.org\/10.1017\/fms.2016.28","journal-title":"Forum of Mathematics, Sigma"},{"issue":"3","key":"3031_CR17","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/0095-8956(82)90046-6","volume":"33","author":"V Neumann-Lara","year":"1982","unstructured":"Neumann-Lara, V.: The dichromatic number of a digraph. J. Combin. Theory Ser. B 33(3), 265\u2013270 (1982)","journal-title":"J. Combin. Theory Ser. B"},{"issue":"5","key":"3031_CR18","doi-asserted-by":"publisher","first-page":"1134","DOI":"10.1016\/j.jctb.2012.05.004","volume":"102","author":"M Pontecorvi","year":"2012","unstructured":"Pontecorvi, M., Wollan, P.: Disjoint cycles intersecting a set of vertices. J. Combin. Theory Ser. B 102(5), 1134\u20131141 (2012)","journal-title":"J. Combin. Theory Ser. B"},{"issue":"1","key":"3031_CR19","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1002\/jgt.23020","volume":"105","author":"R Steiner","year":"2024","unstructured":"Steiner, R.: Subdivisions with congruence constraints in digraphs of large chromatic number. J. Graph Theory 105(1), 136\u2013143 (2024)","journal-title":"J. Graph Theory"},{"issue":"2","key":"3031_CR20","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1002\/jgt.3190070215","volume":"7","author":"C Thomassen","year":"1983","unstructured":"Thomassen, C.: Graph decomposition with applications to subdivisions and path systems modulo $$k$$. J. Graph Theory 7(2), 261\u2013271 (1983)","journal-title":"J. Graph Theory"},{"issue":"1","key":"3031_CR21","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/S0195-6698(85)80025-1","volume":"6","author":"C Thomassen","year":"1985","unstructured":"Thomassen, C.: Even cycles in directed graphs. European J. Combin. 6(1), 85\u201389 (1985)","journal-title":"European J. Combin."},{"issue":"3","key":"3031_CR22","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/s004930100006","volume":"21","author":"C Thomassen","year":"2001","unstructured":"Thomassen, C.: Totally odd $$K_4$$-subdivisions in 4-chromatic graphs. Combinatorica 21(3), 417\u2013443 (2001)","journal-title":"Combinatorica"},{"issue":"2","key":"3031_CR23","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1023\/A:1009784115916","volume":"2","author":"W Zang","year":"1998","unstructured":"Zang, W.: Proof of toft\u2019s conjecture: every graph containing no fully odd $$K_4$$ is $$3$$-colorable. J. Comb. Optim. 2(2), 117\u2013188 (1998)","journal-title":"J. Comb. Optim."}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-026-03031-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-026-03031-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-026-03031-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T06:16:07Z","timestamp":1775715367000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-026-03031-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,4]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["3031"],"URL":"https:\/\/doi.org\/10.1007\/s00373-026-03031-x","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"value":"0911-0119","type":"print"},{"value":"1435-5914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,4]]},"assertion":[{"value":"7 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 February 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2026","order":3,"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 they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}}],"article-number":"32"}}