Bounds on the chromatic number of intersection graphs of sets in the plane
نویسندگان
چکیده
منابع مشابه
Some lower bounds for the $L$-intersection number of graphs
For a set of non-negative integers~$L$, the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots, l}$ to vertices $v$, such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...
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Let G be the intersection graph of a finite family of convex sets obtained by translations of a fixed convex set in the plane. We show that every such graph with clique number k is (3k − 3)-degenerate. This bound is sharp. As a consequence, we derive that G is (3k − 2)-colorable. We show also that the chromatic number of every intersection graph H of a family of homothetic copies of a fixed con...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00501-0