Induced trees in graphs of large chromatic number
نویسندگان
چکیده
منابع مشابه
Induced Colorful Trees and Paths in Large Chromatic Graphs
In a proper vertex coloring of a graph a subgraph is colorful if its vertices are colored with different colors. It is well-known that in every proper coloring of a k-chromatic graph there is a colorful path Pk on k vertices. If the graph is k-chromatic and triangle-free then in any proper coloring there is also a path Pk which is an induced subgraph. N.R. Aravind conjectured that these results...
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Gyárfás and Sumner independently conjectured that for every tree T and integer k there is an integer f(k, T ) such that every graph G with χ(G) > f(k, T ) contains either Kk or an induced copy of T . We prove a ‘topological’ version of the conjecture: for every tree T and integer k there is g(k, T ) such that every graph G with χ(G) > g(k, T ) contains either Kk or an induced copy of a subdivis...
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We investigate which graphs H have the property that in every graph with bounded clique number and sufficiently large chromatic number, some induced subgraph is isomorphic to a subdivision of H. In an earlier paper [6], one of us proved that every tree has this property; and in another earlier paper with M. Chudnovsky [2], we proved that every cycle has this property. Here we give a common gene...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 1997
ISSN: 0364-9024,1097-0118
DOI: 10.1002/(sici)1097-0118(199704)24:4<297::aid-jgt2>3.3.co;2-x