On the existence of two non-neighboring subgraphs in a graph
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Does there exist a functionf(r, n) such that each graphG with Z (G)≧f(r, n) contains either a complete subgraph of orderr or else two non-neighboringn-chromatic subgraphs? It is known thatf(r, 2) exists and we establish the existence off(r, 3). We also give some interesting results about graphs which do not contain two independent edges.
AMS subject classification (1980)05 C 15
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