{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T05:46:28Z","timestamp":1778823988323,"version":"3.51.4"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For given graphs $H_{1}, H_{2}, H_{3}$, the 3-color Ramsey number $R(H_{1},$ $H_{2}, H_{3})$ is the smallest integer $n$ such that if we arbitrarily color the edges of the complete graph of order $n$ with $3$ colors, then it always contains a monochromatic copy of\u00a0$H_{i}$ colored with $i$, for some $1 \\leq i \\leq 3$.We study the bounds on 3-color Ramsey numbers $R(H_1,H_2,H_3)$, where $H_i$ is an isolate-free graph different from $K_2$ with at most four vertices, establishing that $R(P_4,C_4,K_4)=14$, $R(C_4,K_3,K_4-e)=17$, $R(C_4,K_3+e,K_4-e)=17$, $R(C_4,K_4-e,K_4-e)=19$, $28\\le R(C_4,K_4-e,K_4)\\le36$, $R(K_3,K_4-e,K_4)\\le41$, $R(K_4-e,K_4-e,K_4)\\le59$ and $R(K_4-e,K_4,K_4)\\le113$. Also, we prove that $R(K_3+e,K_4-e,K_4-e)=R(K_3,K_4-e,K_4-e)$, $R(C_4,K_3+e,K_4)\\le\\max\\{R(C_4,K_3,K_4),29\\}\\le32$, $R(K_3+e,K_4-e,K_4)\\le\\max\\{R(K_3,K_4-e,K_4),33\\}\\le41$ and $R(K_3+e,K_4,K_4)\\le\\max\\{R(K_3,K_4,K_4),2R(K_3,K_3,K_4)+2\\}\\le79$.This paper is an extension of the article by Arste, Klamroth, Mengersen [Utilitas Mathematica, 1996].<\/jats:p>","DOI":"10.37236\/2160","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:09:50Z","timestamp":1578712190000},"source":"Crossref","is-referenced-by-count":2,"title":["Three Color Ramsey Numbers for Graphs with at most 4 Vertices"],"prefix":"10.37236","volume":"19","author":[{"given":"Luis","family":"Boza","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Janusz","family":"Dybizba\u0144ski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomasz","family":"Dzido","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,12,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p47\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p47\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:21:17Z","timestamp":1579299677000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i4p47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,31]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,10,18]]}},"URL":"https:\/\/doi.org\/10.37236\/2160","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,31]]},"article-number":"P47"}}