Maximum edge-cuts in Cubic Graphs With Large Girth and in Random Cubic Graphs
Résumé
We show that for every cubic graph G with sufficiently large girth there exists a probability distribution on edge-cuts in G such that each edge is in a randomly chosen cut with probability at least 0.88672. This implies that G contains an edge-cut of size at least 1.33008n, where n is the number of vertices of G, and has fractional cut covering number at most 1.127752. The lower bound on the size of maximum edge-cut also applies to random cubic graphs. Specifically, a random n-vertex cubic graph a.a.s. contains an edge-cut of size 1.33008n − o(n).
Domaines
Mathématique discrète [cs.DM]
Origine : Fichiers produits par l'(les) auteur(s)
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