{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:05:29Z","timestamp":1740107129369,"version":"3.37.3"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T00:00:00Z","timestamp":1732752000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T00:00:00Z","timestamp":1732752000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["524418"],"award-info":[{"award-number":["524418"]}],"id":[{"id":"10.13039\/100000893","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":[[2024,12]]},"DOI":"10.1007\/s00373-024-02869-3","type":"journal-article","created":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T09:47:50Z","timestamp":1732787270000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Extremal Graphs for Widom\u2013Rowlinson Colorings in k-Chromatic Graphs"],"prefix":"10.1007","volume":"40","author":[{"given":"John","family":"Engbers","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0628-9322","authenticated-orcid":false,"given":"Aysel","family":"Erey","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,11,28]]},"reference":[{"key":"2869_CR1","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.jctb.2016.03.004","volume":"121","author":"N Alon","year":"2016","unstructured":"Alon, N., Shikhelman, C.: Many $$T$$ copies in $$H$$-free graphs. J. Combin. Theory Ser. B 121, 146\u2013172 (2016)","journal-title":"J. Combin. Theory Ser. B"},{"key":"2869_CR2","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1006\/jctb.1999.1899","volume":"77","author":"G Brightwell","year":"1999","unstructured":"Brightwell, G., Winkler, P.: Graph homomorphisms and phase transitions. J. Combin. Theory Ser. B 77, 415\u2013435 (1999)","journal-title":"J. Combin. Theory Ser. B"},{"key":"2869_CR3","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.ejc.2016.11.003","volume":"62","author":"E Cohen","year":"2017","unstructured":"Cohen, E., Csikv\u00e1ri, P., Perkins, W., Tetali, P.: The Widom\u2013Rowlinson model, the hard-core model and the extremality of the complete graph. Eur. J. Combin. 62, 70\u201376 (2017)","journal-title":"Eur. J. Combin."},{"issue":"2","key":"2869_CR4","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1017\/S0963548316000249","volume":"26","author":"E Cohen","year":"2017","unstructured":"Cohen, E., Perkins, W., Tetali, P.: On the Widom\u2013Rowlinson occupancy fraction in regular graphs. Combin. Probab. Comput. 26(2), 183\u2013194 (2017)","journal-title":"Combin. Probab. Comput."},{"key":"2869_CR5","unstructured":"Csikv\u00e1ri, P.: Extremal regular graphs: the case of the infinite regular tree (2016). arXiv:1612.01295"},{"key":"2869_CR6","doi-asserted-by":"crossref","unstructured":"Csikv\u00e1ri, P., Lin, Z.: Graph homomorphisms between trees. Electron. J. Combin. 21(4), #P4.9 (2014)","DOI":"10.37236\/4096"},{"key":"2869_CR7","doi-asserted-by":"crossref","unstructured":"Csikv\u00e1ri, P., Lin, Z.: Sidorenko\u2019s conjecture, colorings and independent sets. Electron. J. Combin. 24, P1.2 (2017)","DOI":"10.37236\/6019"},{"issue":"4","key":"2869_CR8","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1002\/jgt.20530","volume":"67","author":"J Cutler","year":"2011","unstructured":"Cutler, J., Radcliffe, A.J.: Extremal graphs for homomorphisms. J. Graph Theory 67(4), 261\u2013284 (2011)","journal-title":"J. Graph Theory"},{"key":"2869_CR9","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1002\/jgt.21820","volume":"79","author":"J Engbers","year":"2015","unstructured":"Engbers, J.: Extremal $$H$$-colorings of graphs with fixed minimum degree. J. Graph Theory 79, 103\u2013124 (2015)","journal-title":"J. Graph Theory"},{"key":"2869_CR10","doi-asserted-by":"publisher","first-page":"1347","DOI":"10.1007\/s00373-018-1951-3","volume":"34","author":"J Engbers","year":"2018","unstructured":"Engbers, J., Erey, A.: Extremal colorings and independent sets. Graphs Combin. 34, 1347\u20131361 (2018)","journal-title":"Graphs Combin."},{"issue":"2","key":"2869_CR11","doi-asserted-by":"publisher","first-page":"1478","DOI":"10.1137\/19M1306646","volume":"35","author":"J Engbers","year":"2021","unstructured":"Engbers, J., Erey, A., Fox, J., He, X.: Tomescu\u2019s graph coloring conjecture for $$\\ell $$-connected graphs. SIAM J. Discrete Math. 35(2), 1478\u20131502 (2021)","journal-title":"SIAM J. Discrete Math."},{"key":"2869_CR12","doi-asserted-by":"publisher","first-page":"800","DOI":"10.1016\/j.jctb.2016.09.009","volume":"122","author":"J Engbers","year":"2017","unstructured":"Engbers, J., Galvin, D.: Extremal $$H$$-colorings of trees and 2-connected graphs. J. Combin. Theory Ser. B 122, 800\u2013814 (2017)","journal-title":"J. Combin. Theory Ser. B"},{"key":"2869_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2021.112376","volume":"344","author":"J Engbers","year":"2021","unstructured":"Engbers, J., Keough, L., Short, T.: Independent sets in $$n$$-vertex $$k$$-chromatic $$\\ell $$-connected graphs. Discrete Math. 344, 112376 (2021)","journal-title":"Discrete Math."},{"key":"2869_CR14","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1016\/j.jctb.2018.10.005","volume":"136","author":"J Fox","year":"2019","unstructured":"Fox, J., He, X., Manners, F.: A proof of Tomescu\u2019s graph coloring conjecture. J. Combin. Theory Ser. B 136, 204\u2013221 (2019)","journal-title":"J. Combin. Theory Ser. B"},{"issue":"1","key":"2869_CR15","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1002\/jgt.21658","volume":"73","author":"D Galvin","year":"2013","unstructured":"Galvin, D.: Maximizing $$H$$-colorings of a regular graph. J. Graph Theory 73(1), 66\u201384 (2013)","journal-title":"J. Graph Theory"},{"key":"2869_CR16","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1007\/BF01163705","volume":"38","author":"A Sidorenko","year":"1985","unstructured":"Sidorenko, A.: Proof of London\u2019s conjecture on sums of elements of positive matrices. Math. Notes 38, 716\u2013717 (1985)","journal-title":"Math. Notes"},{"key":"2869_CR17","first-page":"1124","volume":"273","author":"I Tomescu","year":"1971","unstructured":"Tomescu, I.: Le nombre des graphes connexes k-chromatiques minimaux aux sommets \u00e9tiquet\u00e9s. C. R. Acad. Sci. Paris 273, 1124\u20131126 (1971)","journal-title":"C. R. Acad. Sci. Paris"},{"key":"2869_CR18","unstructured":"Tomescu, I.: Introduction to Combinatorics. Collet\u2019s (Publishers) Ltd., London (1975)"},{"key":"2869_CR19","doi-asserted-by":"publisher","first-page":"1670","DOI":"10.1063\/1.1673203","volume":"52","author":"B Widom","year":"1970","unstructured":"Widom, B., Rowlinson, J.S.: New model for the study of liquid-vapor phase transitions. J. Chem. Phys. 52, 1670\u20131684 (1970)","journal-title":"J. Chem. Phys."},{"key":"2869_CR20","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/j.aml.2009.11.005","volume":"23","author":"K Xu","year":"2010","unstructured":"Xu, K.: On the Hosoya index and the Merrifield\u2013Simmons index of graphs with a given clique number. Appl. Math. Lett. 23, 395\u2013398 (2010)","journal-title":"Appl. Math. Lett."}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-024-02869-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-024-02869-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-024-02869-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T20:07:57Z","timestamp":1733515677000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-024-02869-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,28]]},"references-count":20,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["2869"],"URL":"https:\/\/doi.org\/10.1007\/s00373-024-02869-3","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"type":"print","value":"0911-0119"},{"type":"electronic","value":"1435-5914"}],"subject":[],"published":{"date-parts":[[2024,11,28]]},"assertion":[{"value":"14 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 November 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 November 2024","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 have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"134"}}