Total Colorings of Embedded Graphs with No 3-Cycles Adjacent to 4-Cycles
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 4, pp. 977-989
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A total-k-coloring of a graph G is a coloring of V ∪ E using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ′′(G) of G is the smallest integer k such that G has a total-k-coloring. Let G be a graph embedded in a surface of Euler characteristic ε ≥ 0. If G contains no 3-cycles adjacent to 4-cycles, that is, no 3-cycle has a common edge with a 4-cycle, then χ′′(G) ≤ max8, Δ+1.
Keywords:
total coloring, embedded graph, cycle
@article{DMGT_2018_38_4_a7,
author = {Wang, Bing and Wu, Jian-Liang and Sun, Lin},
title = {Total {Colorings} of {Embedded} {Graphs} with {No} {3-Cycles} {Adjacent} to {4-Cycles}},
journal = {Discussiones Mathematicae. Graph Theory},
pages = {977--989},
publisher = {mathdoc},
volume = {38},
number = {4},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGT_2018_38_4_a7/}
}
TY - JOUR AU - Wang, Bing AU - Wu, Jian-Liang AU - Sun, Lin TI - Total Colorings of Embedded Graphs with No 3-Cycles Adjacent to 4-Cycles JO - Discussiones Mathematicae. Graph Theory PY - 2018 SP - 977 EP - 989 VL - 38 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGT_2018_38_4_a7/ LA - en ID - DMGT_2018_38_4_a7 ER -
%0 Journal Article %A Wang, Bing %A Wu, Jian-Liang %A Sun, Lin %T Total Colorings of Embedded Graphs with No 3-Cycles Adjacent to 4-Cycles %J Discussiones Mathematicae. Graph Theory %D 2018 %P 977-989 %V 38 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMGT_2018_38_4_a7/ %G en %F DMGT_2018_38_4_a7
Wang, Bing; Wu, Jian-Liang; Sun, Lin. Total Colorings of Embedded Graphs with No 3-Cycles Adjacent to 4-Cycles. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 4, pp. 977-989. http://geodesic.mathdoc.fr/item/DMGT_2018_38_4_a7/