Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2014

Strong parity vertex coloring of plane graphs

Abstract

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).
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Dates and versions

hal-01063684 , version 1 (15-09-2014)

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Tomas Kaiser, Ondrej Rucky, Matej Stehlik, Riste Škrekovski. Strong parity vertex coloring of plane graphs. Discrete Mathematics and Theoretical Computer Science, 2014, Vol. 16 no. 1 (1), pp.143-158. ⟨10.46298/dmtcs.1268⟩. ⟨hal-01063684⟩
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