{"paper":{"title":"Erd\\H{o}s-Lov\\'asz Tihany Conjecture for graphs with forbidden holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zi-Xia Song","submitted_at":"2018-05-27T14:05:48Z","abstract_excerpt":"A hole in a graph is an induced cycle of length at least $4$. Let $s\\ge2$ and $t\\ge2$ be integers. A graph $G$ is $(s,t)$-splittable if $V(G)$ can be partitioned into two sets $S$ and $T$ such that $\\chi(G[S ]) \\ge s$ and $\\chi(G[T ]) \\ge t$. The well-known Erd\\H{o}s-Lov\\'asz Tihany Conjecture from 1968 states that every graph $G$ with $\\omega(G) < \\chi(G) = s + t - 1$ is $(s,t)$-splittable. This conjecture is hard, and few related results are known. However, it has been verified to be true for line graphs, quasi-line graphs, and graphs with independence number $2$. In this paper, we establish"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11437","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}