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

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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 Hk = {G: every block of G has at most k vertices}. The class Hk 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 Hk.

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