Vertex Covers by Edge Disjoint Cliques

Dedicated to the memory of Paul Erdős

Let 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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Received October 31, 1999


ID="*" Supported in part by NSF grant DMS-9627408.


ID="†" Supported in part by NSF grant CCR-9530974.


ID="‡" Supported in part by OTKA Grants T 030059 and T 29074, FKFP 0607/1999 and by the Bolyai Foundation.


ID="§" Supported in part by NSF grant DMS-9970622.

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Bohman, T., Frieze, A., Ruszinkó, M. et al. Vertex Covers by Edge Disjoint Cliques. Combinatorica 21, 171–197 (2001).

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  • AMS Subject Classification (2000) Classes:  05C80, 05C35