A sufficient condition for edge 6-colorable planar graphs with maximum degree 6

A sufficient condition for edge 6-colorable planar graphs with maximum degree 6

Vizing’s planar graph conjecture remains open for planar graphs with maximum degree 6. In this note, we prove that if each triangle of a planar graph G with maximum degree 6 has a vertex incident with only one triangle, then the chromatic index of G is 6 which means that G is of class one.

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Veröffentlicht in:Discrete Applied Mathematics 2022-05, Vol.313, p.67-70
Hauptverfasser: Lu, Zhengrong, Shi, Lingsheng
Format: Artikel
Sprache:eng
Schlagworte:
Chromatic index
Edge coloring
Graph coloring
Graphs
Maximum degree
Planar graph
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Zusammenfassung:Vizing’s planar graph conjecture remains open for planar graphs with maximum degree 6. In this note, we prove that if each triangle of a planar graph G with maximum degree 6 has a vertex incident with only one triangle, then the chromatic index of G is 6 which means that G is of class one.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2022.01.018