Incidence, a Scoring Positional Game on Graphs

Autor: Bagan, Guillaume, Deschamps, Quentin, Duchêne, Eric, Durain, Bastien, Effantin, Brice, Gledel, Valentin, Oijid, Nacim, Parreau, Aline

Positional games have been introduced by Hales and Jewett in 1963 and have been extensively investigated in the literature since then. These games are played on a hypergraph where two players alternately select an unclaimed vertex of it. In the Maker

Externí odkaz: http://arxiv.org/abs/2211.01083

A characterization of b-chromatic and partial Grundy numbers by induced subgraphs

Autor: Effantin, Brice, Gastineau, Nicolas, Togni, Olivier

Publikováno v: Discrete Mathematics, Elsevier, 2016, 339 (8)

Gy{\'a}rf{\'a}s et al. and Zaker have proven that the Grundy number of a graph $G$ satisfies $\Gamma(G)\ge t$ if and only if $G$ contains an induced subgraph called a $t$-atom.The family of $t$-atoms has bounded order and contains a finite number of

Externí odkaz: http://arxiv.org/abs/1505.07780

[formula omitted]-coloring of trees and bipartite graphs

Autor: Dekar, Lyes, Effantin, Brice, Kheddouci, Hamamache

Publikováno v: In Discrete Mathematics 2010 310(2):260-269

A note on Grundy colorings of central graphs

Autor: Effantin, Brice

Publikováno v: The Australasian Journal of Combinatorics
The Australasian Journal of Combinatorics, Combinatorial Mathematics Society of Australasia (Inc.), 2017, 68 (3), pp.346-356

International audience; A Grundy coloring of a graph G is a proper vertex coloring of G where any vertex x, colored with c(x), has a neighbor of any color 1,2,...,c(x)-1. A central graph G^c is obtained from G by adding an edge between any two non ad

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::98982b0bd3fa277a069132fa4742e8f5
https://hal.archives-ouvertes.fr/hal-01528755

The b-chromatic number of some power graphs.

Autor: Effantin, Brice¹ brice.effantin@u-bourgogne.fr, Kheddouci, Hamamache¹ kheddouc@u-bourgogne.fr

Publikováno v: Discrete Mathematics & Theoretical Computer Science (DMTCS). Dec2003, Vol. 6 Issue 2, p45-54. 10p. 7 Diagrams.