Total coloring of planar graphs of maximum degree eight
In: Information processing letters, Jg. 110 (2010), Heft 8-9, S. 321-324
academicJournal
- print, 7 ref
Zugriff:
The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ(G). It is known that if a planar graph G has maximum degree Δ ≥ 9, then χ(G) = Δ + 1. Recently Hou et al. (Graphs and Combinatorics 24 (2008) 91-100) proved that if G is a planar graph with maximum degree 8 and with either no 5-cycles or no 6-cycles, then χ(G) = 9. In this Note, we strengthen this result and prove that if G is a planar graph with maximum degree 8, and for each vertex x, there is an integer kxE {3, 4, 5, 6, 7, 8} such that there is no kx-cycle which contains x, then χ(G) = 9.
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Total coloring of planar graphs of maximum degree eight
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Autor/in / Beteiligte Person: | ROUSSEL, Nicolas ; XUDING, ZHU |
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Zeitschrift: | Information processing letters, Jg. 110 (2010), Heft 8-9, S. 321-324 |
Veröffentlichung: | Amsterdam: Elsevier, 2010 |
Medientyp: | academicJournal |
Umfang: | print, 7 ref |
ISSN: | 0020-0190 (print) |
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