no. 3
Edge-disjoint odd cycles in graphs with small chromatic number
Annales de l'Institut Fourier, Tome 49 (1999) no. 3, pp. 783-786.

On considère pour un graphe simple le nombre minimum d’arêtes dont l’élimination détruit tous les cycles impairs, et le nombre maximum de cycles impairs qui sont disjoints au sens des arêtes. Quand ces deux coefficients sont égaux, le graphe présente des propriétés intéressantes en relation avec le nombre chromatique.

For a simple graph, we consider the minimum number of edges which block all the odd cycles and the maximum number of odd cycles which are pairwise edge-disjoint. When these two coefficients are equal, interesting consequences appear. Similar problems (but interchanging “vertex-disjoint odd cycles” and “edge-disjoint odd cycles”) have been considered in a paper by Berge and Fouquet.

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Berge, Claude; Reed, Bruce. Edge-disjoint odd cycles in graphs with small chromatic number. Annales de l'Institut Fourier, Tome 49 (1999) no. 3, pp. 783-786. doi : 10.5802/aif.1691. http://www.numdam.org/articles/10.5802/aif.1691/

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[8] B. Reed, Mango and Blueberries (to appear).

[9] B. Reed, Tree widht and tangles, a new measure of connectivity and some applications, Survey in Combinatorics, R. Bailey editor, London Math. Soc. Lecture Notes Series 241, Cambridge University Press, Cambridge 1997, 87-162. | Zbl

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