On the lightness of chordal 4-cycle in 1-planar graphs with high minimum degree

Xin Zhang, Guizhen Liu

Abstract


A graph G is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. The family of 1-planar graphs with minimum vertex degree at least δ and minimum edge degree at least ɛ is denoted by Pδ1(ɛ). In this paper, it is proved that every graph in P71(14) (resp. P61(13)) contains a copy of chordal 4-cycle with all vertices of degree at most 10 (resp. 12).


Keywords


1-planar graph, lightness, cycle, discharging

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DOI: https://doi.org/10.26493/1855-3974.297.fa1

ISSN: 1855-3974

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