{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T19:44:12Z","timestamp":1767987852353,"version":"3.49.0"},"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 two variations of the Gy\u00e1rf\u00e1s-Lehel conjecture on the minimum number of monochromatic components needed to cover an edge-coloured complete bipartite graph. Specifically, we show the following.\r\n\r\nFor $p\\gg (\\log n\/n)^{1\/2}$, w.h.p. every $2$-colouring of the random bipartite graph $G\\sim G(n,n,p)$ admits a cover of all but $O(1\/p)$ vertices of $G$ using at most three vertex-disjoint monochromatic components.\r\nFor every 2-colouring of a bipartite graph $G$ with parts of size $n$ and minimum degree $(13\/16+o(1))n$, the vertices of $G$ can be covered using at most three vertex-disjoint monochromatic components.\r\n\r\n\u00a0<\/jats:p>","DOI":"10.37236\/12937","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:32:32Z","timestamp":1767969152000},"source":"Crossref","is-referenced-by-count":0,"title":["Monochromatic Partitions in 2-Edge-Coloured Bipartite Graphs"],"prefix":"10.37236","volume":"33","author":[{"given":"Camila","family":"Fern\u00e1ndez","sequence":"first","affiliation":[]},{"given":"Mat\u00edas","family":"Pavez-Sign\u00e9","sequence":"additional","affiliation":[]},{"given":"Maya","family":"Stein","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,1,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:32:32Z","timestamp":1767969152000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/12937","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,9]]},"article-number":"P1.6"}}