×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.