Strong products of χ–critical graphs
نویسنده
چکیده
This upper bound is used to calculate several chromatic numbers of strong products. It is shown in particular that for k ≥ 2, χ(C5 2 ×C5 2 ×C2k+1) = 10 + d 5 ke, and for k ≥ 2 and n ≥ 1, χ(C2k+1 2 ×Kn) = k n + d2 e. That the general upper bound cannot be improved for graphs which are not χ–critical is demonstrated by two infinite series of graphs. The paper is concluded with an application to graph retracts: if for some graph H with at least one edge χ(G[H]) = χ(G) χ(H), then no χ–critical subgraph G′ of G, G′ 6= Kn, is a retract of G.
منابع مشابه
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