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    A new upper bound for the clique cover number with applications

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    Let α(G)\alpha(G) and β(G)\beta(G), denote the size of a largest independent set and the clique cover number of an undirected graph GG. Let HH be an interval graph with V(G)=V(H)V(G)=V(H) and E(G)E(H)E(G)\subseteq E(H), and let ϕ(G,H)\phi(G,H) denote the maximum of β(G[W])α(G[W]){\beta(G[W])\over \alpha(G[W])} overall induced subgraphs G[W]G[W] of GG that are cliques in HH. The main result of this paper is to prove that for any graph GG β(G)2α(H)ϕ(G,H)(logα(H)+1),{\beta(G)}\le 2 \alpha(H)\phi(G,H)(\log \alpha(H)+1), where, α(H)\alpha(H) is the size of a largest independent set in HH. We further provide a generalization that significantly unifies or improves some past algorithmic and structural results concerning the clique cover number for some well known intersection graphs
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