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Discussiones Mathematicae Graph Theory 30(3) (2010) 499-533
DOI: https://doi.org/10.7151/dmgt.1510

COLOURING GAME AND GENERALIZED COLOURING GAME ON GRAPHS WITH CUT-VERTICES

Elżbieta Sidorowicz

Faculty of Mathematics, Computer Science and Econometrics
University of Zielona Góra
Z. Szafrana 4a, 65-516 Zielona Góra, Poland
e-mail: e.sidorowicz@wmie.uz.zgora.pl

Abstract

For k ≥ 2 we define a class of graphs H_k = {G: every block of G has at most k vertices}. The class H_k contains among other graphs forests, Husimi trees, line graphs of forests, cactus graphs. We consider the colouring game and the generalized colouring game on graphs from H_k.

Keywords: colouring game, generalized colouring game.

2010 Mathematics Subject Classification: 05C15, 05C57.

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Received 27 May 2010
Revised 28 June 2010
Accepted 28 June 2010