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Recent results on graphical enumeration,We present four of our counting results which are to appear soon in various journals. These comprise: (1) the number of caterpillars, (2) the number of self-complementary configurations, (3) the number of achiral trees, and (4) the probability of an endpoint in a large random tree. We conclude with a brief mention of four miscellaneous results.

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Chromatically equivalent graphs,Let G,H be graphs, and P(G,λ), P(H,λ) be the chromatic polynomials of G,H respectively. Then ., (written P .H), if P(G,λ) = P(H,λ)..In this paper, we first state some open questions relating to chromatic equivalence of graphs, and then give non-trivial examples of chromatically equivalent graphs and their chromatic polynomials.

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吸氣

On the ramsey number of the five-spoked wheel,Let r(W.) be the smallest n such that the five-spoked wheel W. √ G or else W. √ . for every graph G with n vertices. Recently, Erd?s asked whether whether r(W.) ≥ 18; we prove that 17 ≤ r(W.) ≤ 20. In so doing, we establish that r(C., W.) = 13. We conjecture that r(W.) = 20.

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Graphs and Combinatorics978-3-540-37809-9Series ISSN 0075-8434 Series E-ISSN 1617-9692

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