Note: Total coloring of planar graphs with 7-cycles containing at most two chords

Authors:
Renyu Xu;Jian-Liang Wu
Affiliations:
-;-
Venue:
Theoretical Computer Science
Year:
2014

Citing 7
Cited 1

The total chromatic number of any multigraph with maximum degree five is at most seven

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Total-Coloring of Plane Graphs with Maximum Degree Nine

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Total coloring of planar graphs of maximum degree eight

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Total colorings of planar graphs with maximum degree 8 and without 5-cycles with two chords

Theoretical Computer Science

Total coloring of planar graphs with maximum degree 8

Theoretical Computer Science

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Abstract

A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color. In this paper, we prove that if G is a planar graph with maximum degree at least 8 and if every 7-cycle of G contains at most two chords, then G has a (@D+1)-total-coloring.