A new upper bound for the clique cover number with applications
نویسنده
چکیده
Let α(G) and β(G), denote the size of a largest independent set and the clique cover number of an undirected graph G. Let H be an interval graph with V (G) = V (H) and E(G) ⊆ E(H), and let φ(G,H) denote the maximum of β(G[W ]) α(G[W ]) overall induced subgraphs G[W ] of G that are cliques in H . The main result of this paper is to prove that for any graph G β(G) ≤ 2α(H)φ(G,H)(logα(H) + 1), where, α(H) is the size of a largest independent set in H . 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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عنوان ژورنال:
- CoRR
دوره abs/1502.06168 شماره
صفحات -
تاریخ انتشار 2015