Relaxed DP-coloring and another generalization of DP-coloring on planar graphs without 4-cycles and 7-cycles
نویسندگان
چکیده
منابع مشابه
Equitable ∆-Coloring of Planar Graphs without 4-cycles
In this paper, we prove that if G is a planar graph with maximum degree ∆ ≥ 7 and without 4-cycles, then G is equitably m-colorable for any m≥ ∆.
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Let G be a planar graph without 4-cycles and 5-cycles and with maximum degree ∆ ≥ 32. We prove that χ`(G ) ≤ ∆ + 3. For arbitrarily large maximum degree ∆, there exist planar graphs G∆ of girth 6 with χ(G 2 ∆) = ∆ + 2. Thus, our bound is within 1 of being optimal. Further, our bound comes from coloring greedily in a good order, so the bound immediately extends to online list-coloring. In additi...
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An incidence of an undirected graph G is a pair (v, e) where v is a vertex of G and e an edge of G incident with v. Two incidences (v, e) and (w, f) are adjacent if one of the following holds: (i) v = w, (ii) e = f or (iii) vw = e or f . An incidence coloring of G assigns a color to each incidence of G in such a way that adjacent incidences get distinct colors. In 2012, Yang [15] proved that ev...
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A graph G is equitably k-choosable if for any k-uniform list assignment L, G is L-colorable and each color appears on at most d|V (G)|/ke vertices. A graph G is equitable kcolorable if G has a proper vertex coloring with k colors such that the size of the color classes differ by at most 1. In this paper, we prove that if G is a planar graph without 5and 7-cycles, then G is equitably k-choosable...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2021
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2405