Author(s)

Suohai Fan, Hongjian Lai, Ju Zhou

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For a graph G, let b(G)=max﹛|D|: Dis an edge cut of G﹜ . For graphs G and H, a map Ψ: V(G)→V(H) is a graph homomorphism if for each e=uv∈E(G), Ψ(u)Ψ(v)∈E(H). In 1979, Erdös proved by probabilistic methods that for p ≥ 2 with if there is a graph homomorphism from G onto K_p then b(G)≥f(p)|E(G)| In this paper, we obtained the best possible lower bounds of b(G) for graphs G with a graph homomorphism onto a Kneser graph or a circulant graph and we characterized the graphs G reaching the lower bounds when G is an edge maximal graph with a graph homomorphism onto a complete graph, or onto an odd cycle.

Maximum Edge Cuts, Graph Homomorphisms

S. Fan, H. Lai and J. Zhou, "The Maximum Size of an Edge Cut and Graph Homomorphisms," Applied Mathematics, Vol. 2 No. 10, 2011, pp. 1263-1269. doi: 10.4236/am.2011.210176.