A strong parity vertex coloring of a 2-connected plane graph is a coloring of the vertices such that every face is incident with zero or an odd number of vertices of each color. We prove that every 2-connected loopless plane graph has a strong parity vertex coloring with 97 colors. Moreover the coloring we construct is proper. This proves a conjecture of Czap and Jendrol' [Discuss. Math. Graph Theory 29 (2009), pp. 521-543.]. We also provide examples showing that eight colors may be necessary (ten when restricted to proper colorings).

Source : oai:HAL:hal-01063684v1

Volume: Vol. 16 no. 1

Section: Graph Theory

Published on: March 20, 2014

Submitted on: January 7, 2011

Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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