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The Maximum Size of an Edge Cut and Graph Homomorphisms

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DOI: 10.4236/am.2011.210176    3,588 Downloads   6,262 Views  

ABSTRACT

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 Kp 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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