The game of arboricity - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2005

The game of arboricity

Abstract

Using a fixed set of colors $C$, Ann and Ben color the edges of a graph $G$ so that no monochromatic cycle may appear. Ann wins if all edges of $G$ have been colored, while Ben wins if completing a coloring is not possible. The minimum size of $C$ for which Ann has a winning strategy is called the $\textit{game arboricity}$ of $G$, denoted by $A_g(G)$. We prove that $A_g(G) \leq 3k$ for any graph $G$ of arboricity $k$, and that there are graphs such that $A_g(G) \geq 2k-2$. The upper bound is achieved by a suitable version of the activation strategy, used earlier for the vertex coloring game. We also provide other strategie based on induction.
Fichier principal
Vignette du fichier
dmAE0113.pdf (108.95 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01184385 , version 1 (14-08-2015)

Identifiers

Cite

Tomasz Bartnicki, Jaroslaw Grytczuk, Hal Kierstead. The game of arboricity. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.63-66, ⟨10.46298/dmtcs.3428⟩. ⟨hal-01184385⟩

Collections

INSMI TDS-MACS
95 View
505 Download

Altmetric

Share

Gmail Facebook X LinkedIn More