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Discussiones Mathematicae Graph Theory 26(1) (2006) 41-48
DOI: https://doi.org/10.7151/dmgt.1299

A CHARACTERIZATION OF PLANAR MEDIAN GRAPHS

Iztok Peterin

Faculty of Electrical Engineering and Computer Science
University of Maribor
Smetanova ulica 17, 2000 Maribor, Slovenia
e-mail: iztok.peterin@uni-mb.si

Abstract

Median graphs have many interesting properties. One of them is-in connection with triangle free graphs-the recognition complexity. In general the complexity is not very fast, but if we restrict to the planar case the recognition complexity becomes linear. Despite this fact, there is no characterization of planar median graphs in the literature. Here an additional condition is introduced for the convex expansion procedure that characterizes planar median graphs.

Keywords: median graphs, planar graphs, expansion.

2000 Mathematics Subject Classification: 05C10, 05C75.

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Received 7 October 2004
Revised 21 April 2005