Discussiones Mathematicae Graph Theory 32(4) (2012) 737-747
doi: 10.7151/dmgt.1639

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On Properties of Maximal 1-planar Graphs

Dávid Hudák, Tomáš Madaras

Institute of Mathematics, Faculty of Sciences
University of P. J. Šafárik
Jesenná 5, 041 54 Košice, Slovak Republic

Yusuke Suzuki

Department of Mathematics, Faculty of Science
Niigata University
8050, Ikarashi 2-no-cho, Nishi-ku, Niigata, 950-2181, Japan

Abstract

A graph is called 1-planar if there exists a drawing in the plane so that each edge contains at most one crossing. We study maximal 1-planar graphs from the point of view of properties of their diagrams, local structure and hamiltonicity.

Keywords: 1-planar graph, maximal graph

2010 Mathematics Subject Classification: 05C10.

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Received 23 May 2011
Revised 17 January 2012
Accepted 18 January 2012