{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:08:13Z","timestamp":1699834093990},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":10451,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1978,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a multigraph G, a sequence (h<jats:sub>1<\/jats:sub>,\u2026, h<jats:sub>m<\/jats:sub>) of nonnegative integers h<jats:sub>1<\/jats:sub> \u2265\u2026 \u2265 h<jats:sub>m<\/jats:sub> is color\u2010feasible for G if there is an edge\u2010coloring H<jats:sub>1<\/jats:sub>,\u2026, H<jats:sub>m<\/jats:sub> where H<jats:sub>i<\/jats:sub> has exactly h<jats:sub>i<\/jats:sub> edges (i=1,\u2026, m). It is known that the set C(G) of color\u2010feasible sequences of G is partially ordered. We show that if G is simple with maximum degree d, then all maximal sequences of C(G) have at most d+1 nonzero entries. This result can be extended to multigraphs. Furthermore, if the odd elementary cycles of a multigraph G satisfy some specified conditions then all maximal sequences have at most d+1 nonzero entries.<\/jats:p>","DOI":"10.1002\/net.3230080105","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T08:20:00Z","timestamp":1178871600000},"page":"7-16","source":"Crossref","is-referenced-by-count":0,"title":["Color\u2010feasible sequences of a multigraph"],"prefix":"10.1002","volume":"8","author":[{"given":"D.","family":"de Werra","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs and Hypergraphs","author":"Berge C.","year":"1973"},{"key":"e_1_2_1_3_2","first-page":"561","volume-title":"Edge Colorings in Bipartite Graphs","author":"Folkman J.","year":"1969"},{"issue":"3","key":"e_1_2_1_4_2","first-page":"311","article-title":"Colorations des Ar\u011btes d'un Graphe","volume":"15","author":"Fournier J. C.","year":"1973","journal-title":"Cahiers du C. E. R. O."},{"key":"e_1_2_1_5_2","volume-title":"M\u00e9thode et Th\u00e9or\u00e8me G\u00e9n\u00e9ral de Coloration des Ar\u011btes d'un Multigraphe","author":"Fournier J. C.","year":"1976"},{"key":"e_1_2_1_6_2","unstructured":"Hilton A. J. W. \u201cA Note on Edge\u2010Colouring Multigraphs \u201dProc. of 2nd Csech. Symp. on Graph Theory 1974 pp.267\u2013271."},{"key":"e_1_2_1_7_2","first-page":"25","article-title":"On an Estimate of the Chromatic Class of a p\u2010Graph","volume":"3","author":"Vizing V. G.","year":"1964","journal-title":"Diskret. Analiz."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(76)90027-7"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(76)90056-X"},{"key":"e_1_2_1_10_2","volume-title":"Color\u2010Feasible Sequences of Almost Bipartite Multigraphs","author":"de Werra D.","year":"1976"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230080105","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230080105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T09:05:11Z","timestamp":1699779911000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230080105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,3]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1978,3]]}},"alternative-id":["10.1002\/net.3230080105"],"URL":"https:\/\/doi.org\/10.1002\/net.3230080105","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,3]]}}}