{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T21:45:32Z","timestamp":1771623932469,"version":"3.50.1"},"reference-count":0,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T00:00:00Z","timestamp":1498694400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201506290097"],"award-info":[{"award-number":["201506290097"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11571135"],"award-info":[{"award-number":["11571135"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671320"],"award-info":[{"award-number":["11671320"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2018,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For an edge\u2010colored graph, its minimum color degree is defined as the minimum number of colors appearing on the edges incident to a vertex and its maximum monochromatic degree is defined as the maximum number of edges incident to a vertex with a same color. A cycle is called properly colored if every two of its adjacent edges have distinct colors. In this article, we first give a minimum color degree condition for the existence of properly colored cycles, then obtain the minimum color degree condition for an edge\u2010colored complete graph to contain properly colored triangles. Afterwards, we characterize the structure of an edge\u2010colored complete bipartite graph without containing properly colored cycles of length 4 and give the minimum color degree and maximum monochromatic degree conditions for an edge\u2010colored complete bipartite graph to contain properly colored cycles of length 4, and those passing through a given vertex or edge, respectively.<\/jats:p>","DOI":"10.1002\/jgt.22163","type":"journal-article","created":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T11:28:35Z","timestamp":1498735715000},"page":"362-373","source":"Crossref","is-referenced-by-count":27,"title":["Color degree and monochromatic degree conditions for short properly colored cycles in edge\u2010colored graphs"],"prefix":"10.1002","volume":"87","author":[{"given":"Shinya","family":"Fujita","sequence":"first","affiliation":[{"name":"International College of Arts and Sciences Yokohama City University, 22\u20102 Seto, Kanazawa\u2010ku Yokohama Kanagawa 236\u20100027 Japan"}]},{"given":"Ruonan","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics Northwestern Polytechnical University Xi'an Shaanxi 710072 P.R.\u00a0China"},{"name":"Faculty of EEMCS University of Twente 7500 AE Enschede The Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9596-0826","authenticated-orcid":false,"given":"Shenggui","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics Northwestern Polytechnical University Xi'an Shaanxi 710072 P.R.\u00a0China"}]}],"member":"311","published-online":{"date-parts":[[2017,6,29]]},"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.22163","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22163","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T19:41:17Z","timestamp":1695930077000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.22163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,29]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,3]]}},"alternative-id":["10.1002\/jgt.22163"],"URL":"https:\/\/doi.org\/10.1002\/jgt.22163","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,6,29]]}}}