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}
}
  • E. Sidorowicz
  • Published 2010
  • Mathematics
  • Discuss. Math. Graph Theory
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. 

Figures from this paper

Characterising and recognising game-perfect graphs

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

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

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

References

SHOWING 1-10 OF 28 REFERENCES

The game chromatic number and the game colouring number of cactuses

Note on the game chromatic index of trees

Relaxed game chromatic number of trees and outerplanar graphs

The Game Coloring Number of Planar Graphs

It is shown that the game coloring number of a planar graph is at most 19, which implies that thegame chromatic number of the game chromatic numbers of planar graphs is at least 19, improved on the previous known upper bound.

A Simple Competitive Graph Coloring Algorithm

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).

Refined activation strategy for the marking game

A bound for the game chromatic number of graphs

Game chromatic number of outerplanar graphs

This note proves that the game chromatic number of an outerplanar graph is at most 7. This improves the previous known upper bound of the game chromatic number of outerplanar graphs. © 1999 John