On the Strong Parity Chromatic Number
نویسندگان
چکیده
A vertex colouring of a 2-connected plane graph G is a strong parity vertex colouring if for every face f and each colour c, the number of vertices incident with f coloured by c is either zero or odd. Czap et al. in [9] proved that every 2-connected plane graph has a proper strong parity vertex colouring with at most 118 colours. In this paper we improve this upper bound for some classes of plane graphs.
منابع مشابه
Strong parity vertex coloring of plane graphs
Czap and Jendrol’ introduced the notions of strong parity vertex coloring and the corresponding strong parity chromatic number χs. They conjectured that there is a constant bound K on χs for the class of 2-connected plane graphs. We prove that the conjecture is true with K = 97, even with an added restriction to proper colorings. Next, we provide simple examples showing that the sharp bound is ...
متن کاملxx ( xxxx ) 1 – 14 2 ON THE STRONG PARITY CHROMATIC NUMBER
12 A vertex colouring of a 2-connected plane graph G is a strong parity 13 vertex colouring if for every face f and each colour c, the number of 14 vertices incident with f coloured by c is either zero or odd. 15 Czap et al. in [9] proved that every 2-connected plane graph has a 16 proper strong parity vertex colouring with at most 118 colours. 17 In this paper we improve this upper bound for s...
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