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

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.

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.

@article{AIF_1999__49_3_783_0,
     author = {Berge, Claude and Reed, Bruce},
     title = {Edge-disjoint odd cycles in graphs with small chromatic number},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {3},
     year = {1999},
     pages = {783-786},
     doi = {10.5802/aif.1691},
     zbl = {0923.05034},
     mrnumber = {2000f:05051},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1999__49_3_783_0}
}
Berge, Claude; Reed, Bruce. Edge-disjoint odd cycles in graphs with small chromatic number. Annales de l'Institut Fourier, Volume 49 (1999) no. 3, pp. 783-786. doi : 10.5802/aif.1691. http://www.numdam.org/item/AIF_1999__49_3_783_0/

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