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Ars Combinatoria

  • Research article

Every \(1\)-Planar Graph without \(4\)-Cycles or Adjacent \(5\)-Vertices is \(5\)-Colorable

Lili Song1, Lei Sun 1
1Department of Mathematics, Shandong Normal University Jinan 250014, China
  • Published: 31/10/2017

Abstract

A graph is \(1\)-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every \(1\)-planar graph without \(4\)-cycles or adjacent \(5\)-vertices is \(5\)-colorable.

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Citation
Lili Song, Lei Sun . Every \(1\)-Planar Graph without \(4\)-Cycles or Adjacent \(5\)-Vertices is \(5\)-Colorable[J], Ars Combinatoria, Volume 135. 29-38. .