Edge Colorings of Planar Graphs Without 6-Cycles with Three Chords

A graph G is of class 1 if its edges can be colored with k colors such that adjacent edges receive different colors, where k is the maximum degree of G . It is proved here that every planar graph is of class 1 if its maximum degree is at least 6 and any 6-cycle contains at most two chords.

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2018-04, Vol.41 (2), p.1077-1084
Main Authors: Zhang, Wenwen, Wu, Jian-Liang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Chords (geometry)
Graph coloring
Graph theory
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Online Access:Get full text
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Description
Summary:A graph G is of class 1 if its edges can be colored with k colors such that adjacent edges receive different colors, where k is the maximum degree of G . It is proved here that every planar graph is of class 1 if its maximum degree is at least 6 and any 6-cycle contains at most two chords.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-016-0376-5