Graphs which, with their complements, have certain clique covering numbers
نویسندگان
چکیده
منابع مشابه
Clique Minors in Graphs and Their Complements
A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. Let t ≥ 1 be an integer, and let G be a graph on n vertices with no minor isomorphic to Kt+1. Kostochka conjectures that there exists a constant c = c(k) independent of G such that the complement of G has a minor isomorphic to Ks, where s = d2 (1 + 1/t)n − ce. We prove that Kostochka’s conjecture i...
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For each m ≥ 1, we construct a graph G = (V, E) with ω(G) = m such that max i=1,2 ω(ind(Vi)) = m for arbitrary partition V = V1 ∪ V2, where ω(G) is the clique number of G and ind(Vi) is the induced graph of Vi. Using this result, we may show that for each m ≥ 2 there exists an exact m-cover of Z which is not the union of two 1-covers.
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Many graph-theoretical problems involve the study of cliques, i .e ., complete subgraphs (not necessarily maximal) . In this context the following combinatorial problem arises naturally: For which numbers n and c is there a graph with n vertices and exactly c cliques? For fixed n, let G(n) denote the set of all such `clique numbers' c . Since each singleton and the empty set are always cliques,...
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The edge clique cover sum number (resp. edge clique partition sum number) of a graph G, denoted by scc(G) (resp. scp(G)), is defined as the smallest integer k for which there exists a collection of complete subgraphs of G, covering (resp. partitioning) all edges of G such that the sum of sizes of the cliques is at most k. By definition, scc(G) 5 scp(G). Also, it is known that for every graph G ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1981
ISSN: 0012-365X
DOI: 10.1016/0012-365x(81)90016-9