{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T18:28:56Z","timestamp":1773944936342,"version":"3.50.1"},"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>Scott proved in 1997 that for any tree $T$, every graph with bounded\u00a0clique number which does not contain any subdivision of $T$ as an\u00a0induced subgraph has bounded chromatic number. Scott also conjectured\u00a0that the same should hold if $T$ is replaced by any graph $H$. Pawlik\u00a0et al.\u00a0recently constructed a family of triangle-free\u00a0intersection graphs of segments in the plane with unbounded chromatic\u00a0number (thereby disproving an old conjecture of Erd\u0151s). This shows\u00a0that Scott's conjecture is false whenever $H$ is obtained from a\u00a0non-planar graph by subdividing every edge at least once.It remains interesting to decide which graphs $H$ satisfy Scott's\u00a0conjecture and which do not. In this paper, we study the construction\u00a0of Pawlik et al. in more details to extract more counterexamples\u00a0to Scott's conjecture. For example, we show that Scott's conjecture is\u00a0false for any graph obtained from $K_4$ by subdividing every edge at\u00a0least once.\u00a0 We also prove that if $G$ is a 2-connected\u00a0multigraph with no vertex contained in every cycle of $G$, then any\u00a0graph obtained from $G$ by subdividing every edge at least twice is a\u00a0counterexample to Scott's conjecture.<\/jats:p>","DOI":"10.37236\/4424","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:54:21Z","timestamp":1578693261000},"source":"Crossref","is-referenced-by-count":15,"title":["Restricted Frame Graphs and a Conjecture of Scott"],"prefix":"10.37236","volume":"23","author":[{"given":"J\u00e9r\u00e9mie","family":"Chalopin","sequence":"first","affiliation":[]},{"given":"Louis","family":"Esperet","sequence":"additional","affiliation":[]},{"given":"Zhentao","family":"Li","sequence":"additional","affiliation":[]},{"given":"Patrice","family":"Ossona de Mendez","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,2,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p30\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:36:06Z","timestamp":1579239366000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/4424","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,19]]},"article-number":"P1.30"}}