Vertex Covers by Edge Disjoint Cliques

Dedicated to the memory of Paul ErdősLet H be a simple graph having no isolated vertices. An (H,k)-vertex-cover of a simple graph G = (V,E) is a collection of subgraphs of G satisfying 1. , for all i = 1, ..., r, 2. , 3. , for all , and 4.  each is in at most k of the . We consider the existence of such vertex covers when H is a complete graph, , in the context of extremal and random graphs.

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