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ArticleOriginal scientific text

Title

On local structure of 1-planar graphs of minimum degree 5 and girth 4

Authors 1, 1

Affiliations

  1. Institute of Mathematics, Faculty of Sciences, University of P. J. Šafárik, Jesenná 5, 040 01 Košice, Slovak Republic

Abstract

A graph is 1-planar if it can be embedded in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree 5 and girth 4 contains (1) a 5-vertex adjacent to an ≤ 6-vertex, (2) a 4-cycle whose every vertex has degree at most 9, (3) a K1,4 with all vertices having degree at most 11.

Keywords

ENG
light graph, 1-planar graph, star, cycle

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Discussiones Mathematicae Graph Theory
2009/29/2
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Pages:
385-400
Main language of publication
English
Received
2007-11-13
Accepted
2008-07-28
Published
2009

DOI: 10.7151/dmgt.1454

Exact and natural sciences