On local properties of 1-planar graphs with high minimum degree

Dávid Hudák, Tomáš Madaras

Abstract


A graph is called 1-planar if there exists its drawing in the plane such that each edge contains at most one crossing. We prove that each 1-planar graph of minimum degree 7 contains a pair of adjacent vertices of degree 7 as well as several small graphs whose vertices have small degrees; we also prove the existence of a 4-cycle with relatively small degree vertices in 1-planar graphs of minimum degree at least 6.

Keywords


1-planar graph, light graph

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DOI: https://doi.org/10.26493/1855-3974.131.91c

ISSN: 1855-3974

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