# Colouring game and generalized colouring game on graphs with cut-vertices

@article{Sidorowicz2010ColouringGA, title={Colouring game and generalized colouring game on graphs with cut-vertices}, author={Elzbieta Sidorowicz}, journal={Discuss. Math. Graph Theory}, year={2010}, volume={30}, pages={499-533} }

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.

## 3 Citations

### Characterising and recognising game-perfect graphs

- MathematicsDiscret. Math. Theor. Comput. Sci.
- 2019

This work characterise $g_B$-perfect graphs in two ways: by forbidden induced subgraphs and by explicit structural descriptions, and presents a clique module decomposition that allows us to efficiently recognise $ g_B- perfect graphs.

### The edge coloring game on trees with the number of colors greater than the game chromatic index

- MathematicsJ. Comb. Optim.
- 2019

It is proved that, for any [X,–Y], Alice has a winning strategy for the k-[X, Y]-edge-coloring game on any tree T when k>χ[X,Y]′(T).

### The Relaxed Game Chromatic Number of Graphs with Cut-Vertices

- Materials ScienceGraphs and Combinatorics
- 2015

In the (r,d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

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