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Chromatic uniqueness and equivalence of $$K_ 4$$ homeomorphs. (English) Zbl 0555.05035
A formula for the chromatic polynomial of any subdivision of a $$K_ 4$$, also called an $$K_ 4$$ homeomorph, is obtained. It is used to obtain infinite families of pairs of chromatically equivalent (i.e. with the same chromatic polynomial) nonisomorphic $$K_ 4$$ homeomorphs, as well as an infinite family of chromatically unique graphs.
Reviewer: B.Toft

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
K4-homeomorph; chromatic polynomial
Full Text:
##### References:
 [1] Chao, Chromatic polynomials of a family of graphs · Zbl 0532.05027 [2] Graph Theory. Addison-Wesley, Reading, MA (1969). [3] Loerinc, Discrete Math. 23 pp 313– (1978) · Zbl 0389.05034 · doi:10.1016/0012-365X(78)90012-2 [4] Read, J. Combinatorial Theory 4 pp 52– (1968) · Zbl 0165.32802 [5] Zykov, Mat. Sb. 24 pp 163– (1949)
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