{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:56Z","timestamp":1753893836294,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We study the mixed Ramsey number $maxR(n,{K_m},{K_r})$, defined as the maximum number of colours in an edge-colouring of the complete graph $K_n$, such that $K_n$ has no monochromatic complete subgraph on $m$ vertices and no rainbow complete subgraph on $r$ vertices. Improving an upper bound of Axenovich and Iverson, we show that $maxR(n,{K_m},{K_4}) \\leq n^{3\/2}\\sqrt{2m}$ for all $m\\geq 3$. Further, we discuss a possible way to improve their lower bound on $maxR(n,{K_4},{K_4})$ based on incidence graphs of finite projective planes.<\/jats:p>","DOI":"10.37236\/257","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:29:14Z","timestamp":1578698954000},"source":"Crossref","is-referenced-by-count":0,"title":["A Note on Edge-Colourings Avoiding Rainbow $K_4$ and Monochromatic $K_m$"],"prefix":"10.37236","volume":"16","author":[{"given":"Veselin","family":"Jungi\u0107","sequence":"first","affiliation":[]},{"given":"Tom\u00e1\u0161","family":"Kaiser","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"Kr\u00e1l'","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,6,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n19\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T21:52:50Z","timestamp":1579297970000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1n19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/257","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,6,12]]},"article-number":"N19"}}