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Chromatic polynomials, polygon trees, and outerplanar graphs. (English) Zbl 0778.05074
Summary: It is proved that all classes of polygon trees are characterized by their chromatic polynomials, and a characterization is given of those polynomials that are chromatic polynomials of outerplanar graphs. The first result yields an alternative proof that outerplanar graphs are recognizable from their vertex-deleted subgraphs.

MSC:
05C75 Structural characterization of families of graphs
05C05 Trees
05C15 Coloring of graphs and hypergraphs
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References:
[1] Chao, Arch. Math. 45 pp 180– (1985)
[2] Chao, Arch. Math. 43 pp 187– (1984)
[3] Giles, J. Combinat. Theory B 16 pp 215– (1974)
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[5] Woodall, Discrete Math. 101 (1992)
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