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Maximum chromatic polynomials of 2-connected graphs
Authors:Ioan Tomescu
Abstract:In this paper we obtain chromatic polynomials P(G; λ) of 2-connected graphs of order n that are maximum for positive integer-valued arguments λ ≧ 3. The extremal graphs are cycles Cn and these graphs are unique for every λ ≧ 3 and n ≠ 5. We also determine max{P(G; λ): G is 2-connected of order n and GCn} and all extremal graphs relative to this property, with some consequences on the maximum number of 3-colorings in the class of 2-connected graphs of order n having X(G) = 2 and X(G) = 3, respectively. For every n ≧ 5 and λ ≧ 4, the first three maximum chromatic polynomials of 2-connected graphs are determined.
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