# 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.

## 2 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).

## References

SHOWING 1-10 OF 28 REFERENCES

### The game chromatic number and the game colouring number of cactuses

- MathematicsInf. Process. Lett.
- 2007

### Lower bounds for the game colouring number of partial k-trees and planar graphs

- MathematicsDiscret. Math.
- 2008

### A Simple Competitive Graph Coloring Algorithm

- MathematicsJ. Comb. Theory, Ser. B
- 2000

It is proved that the game coloring number, and therefore the game chromatic number, of a planar graph is at most 18, and thegame coloring number of a graph G is bound in terms of a new parameter r(G).

### Game chromatic index of k-degenerate graphs

- MathematicsJ. Graph Theory
- 2001

The game chromatic index of a graph G is the minimum number of colors for which Alice has a winning strategy and is studied in this paper.

### Marking Games and the Oriented Game Chromatic Number of Partial k-Trees

- MathematicsGraphs Comb.
- 2003

The oriented game chromatic number of partial k-trees was bounded positively according to Nešetřil and Sopena and this work answers this question positively.