The Maximum Size of an Edge Cut and Graph Homomorphisms

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 *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.

For a graph

Cite this paper

nullS. 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.

nullS. Fan, H. Lai and J. Zhou, "The Maximum Size of an Edge Cut and Graph Homomorphisms,"

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