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Properties of Descartes' Construction of Triangle-Free Graphs with High Chromatic Number

Published online by Cambridge University Press:  01 September 1999

A. V. KOSTOCHKA
Affiliation:
Institute of Mathematics, 630090, Novosibirsk, Russia (e-mail: sasha@math.nse.ru)
J. NEšETŘIL
Affiliation:
Department of Applied Mathematics, Charles University, Malostranské nám. 25, 11800 Praha 1, Czech Republic (e-mail: nesetril@kam.ms.mff.cuni.cz)

Abstract

We present some nice properties of the classical construction of triangle-free graphs with high chromatic number given by Blanche Descartes and its modifications. In particular, we construct colour-critical graphs and hypergraphs of high girth with moderate average degree.

Type
Research Article
Copyright
1999 Cambridge University Press

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