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Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We investigate the problem of determining how many monochromatic trees are necessary to cover the vertices of an edge-colored random graph. More precisely, we show that for $p\\gg n^{-1\/6}{(\\ln n)}^{1\/6}$, in any $3$-edge coloring of the random graph $G(n,p)$ we can find three monochromatic trees such that their union covers all vertices. This improves, for three colors, a result of Buci\u0107, Kor\u00e1ndi, and Sudakov.<\/jats:p>","DOI":"10.1137\/20m137464x","type":"journal-article","created":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T10:48:22Z","timestamp":1624272502000},"page":"1447-1459","source":"Crossref","is-referenced-by-count":1,"title":["Covering 3-Edge-Colored Random Graphs with Monochromatic Trees"],"prefix":"10.1137","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7841-157X","authenticated-orcid":true,"given":"Yoshiharu","family":"Kohayakawa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Walner","family":"Mendon\u00e7a","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9722-1819","authenticated-orcid":true,"given":"Guilherme Oliveira","family":"Mota","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bjarne","family":"Sch\u00fclke","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,6,21]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s004930170001"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.37236\/6089"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"B. 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Henderson,\n                      Permutation decomposition of (0,1)-matrices and decomposition transversals\n                      , Doctoral dissertation, California Institute of Technology, 1971."},{"key":"atypb13","unstructured":"S. Janson, T. \u0141uczak, and A. Ruci\u0144ski,\n                      Random Graphs\n                      , Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience, New York, 2000."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004117000846"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20819"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M137464X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:45:01Z","timestamp":1787319901000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M137464X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M137464X"],"URL":"https:\/\/doi.org\/10.1137\/20m137464x","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}