Parity vertex coloring of outerplane graphs
نویسندگان
چکیده
منابع مشابه
Facial Parity 9-Edge-Coloring of Outerplane Graphs
A facial parity edge coloring of a 2-edge-connected plane graph is such an edge coloring in which no two face-adjacent edges (consecutive edges of a facial walk of some face) receive the same color, in addition, for each face f and each color c, either no edge or an odd number of edges incident with f is colored with c. It is known that any 2-edgeconnected plane graph has a facial parity edge c...
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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 ...
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A parity path in a vertex colouring of a graph is a path along which each colour is used an even number of times. Let χp(G) be the least number of colours in a proper vertex colouring of G having no parity path. It is proved that for any graph G we have the following tight bounds χ(G) ≤ χp(G) ≤ |V (G)| − α(G) + 1, where χ(G) and α(G) are the chromatic number and the independence number of G, re...
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A parity walk in an edge-coloring of a graph is a walk along which each color is used an even number of times. Let p(G) be the least number of colors in an edge-coloring of G having no parity path (a parity edge-coloring). Let p̂(G) be the least number of colors in an edge-coloring of G having no open parity walk (a strong parity edge-coloring). Always p̂(G) ≥ p(G) ≥ χ′(G). We prove that p̂(Kn) = ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.06.009