{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:00Z","timestamp":1753893840468,"version":"3.41.2"},"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 integers $n\\ge 0$, an iterated triangulation $\\mathrm{Tr}(n)$ is defined recursively as follows: $\\mathrm{Tr}(0)$ is the plane triangulation on three vertices and, for $n\\ge 1$, $\\mathrm{Tr}(n)$ is the plane triangulation obtained from the plane triangulation $\\mathrm{Tr}(n-1)$ by, for each inner face $F$ of $\\mathrm{Tr}(n-1)$, adding inside $F$ a new vertex and three edges joining this new vertex to the three vertices incident with $F$.\r\nIn this paper, we show that there exists a 2-edge-coloring of $\\mathrm{Tr}(n)$ such that $\\mathrm{Tr}(n)$ contains no monochromatic copy of the cycle $C_k$ for any $k\\ge 5$. As a consequence, the answer to one of two questions asked by Axenovich et al. is negative. We also determine the radius 2 graphs $H$ for which there exists $n$ such that every 2-edge-coloring of $\\mathrm{Tr}(n)$ contains a monochromatic copy of $H$, extending a result of Axenovich et al. for radius 2 trees.<\/jats:p>","DOI":"10.37236\/9292","type":"journal-article","created":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T08:55:27Z","timestamp":1604048127000},"source":"Crossref","is-referenced-by-count":0,"title":["Monochromatic Subgraphs in Iterated Triangulations"],"prefix":"10.37236","volume":"27","author":[{"given":"Jie","family":"Ma","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianyun","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingxing","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,10,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p18\/8199","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p18\/8199","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T08:55:27Z","timestamp":1604048127000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,30]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/9292","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,10,30]]},"article-number":"P4.18"}}