Planar graphs without short even cycles are near-bipartite

Planar graphs without short even cycles are near-bipartite

A graph is near-bipartite if its vertex set can be partitioned into an independent set and a set that induces a forest. It is clear that near-bipartite graphs are 3-colorable. In this note, we show that planar graphs without cycles of lengths in {4,6,8} are near-bipartite.

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Veröffentlicht in:Discrete Applied Mathematics 2020-09, Vol.284, p.626-630
Hauptverfasser: Liu, Runrun, Yu, Gexin
Format: Artikel
Sprache:eng
Schlagworte:
3-colorable
Graph theory
Graphs
Near-bipartite
Planar graphs
Vertex sets
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Zusammenfassung:A graph is near-bipartite if its vertex set can be partitioned into an independent set and a set that induces a forest. It is clear that near-bipartite graphs are 3-colorable. In this note, we show that planar graphs without cycles of lengths in {4,6,8} are near-bipartite.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2020.04.017