On the existence of two non-neighboring subgraphs in a graph

Abstract

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.

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El-Zahar, M., Erdős, P. On the existence of two non-neighboring subgraphs in a graph. Combinatorica 5, 295–300 (1985). https://doi.org/10.1007/BF02579243

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AMS subject classification (1980)

  • 05 C 15