Multiple vertex coverings by specified induced subgraphs
Abstract
Given graphs H1,...,Hk, we study the minimum order of a graph G such that for each i, the induced copies of Hi in G cover V(G). We prove a general upper bound of twice the sum of the numbers mi, where mi is one less than the order of Hi. When k=2 and one graph is an independent set of size n, we determine the optimum within a constant. When k=2 and the graphs are a star and an independent set, we determine the answer exactly.
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