Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2014; 51(2): 511-517

Printed March 31, 2014

https://doi.org/10.4134/BKMS.2014.51.2.511

Copyright © The Korean Mathematical Society.

Light 3-cycles in 1-planar graphs with degree restrictions

Xin Zhang

Xidian University

Abstract

In this paper, we prove that the 3-cycle is light in the family of 1-planar graphs with minimum vertex degree at least 5 and minimum edge degree at least 12. This generates a known result of Fabrici and Madaras \cite{Fabrici}.

Keywords: 1-planar graph, light graph, triangle, discharging

MSC numbers: Primary 05C75; Secondary 05C10