Maximum edge-cuts in Cubic Graphs With Large Girth and in Random Cubic Graphs

František Kardoš (1) , Daniel Kráľ (2) , Jan Volec (2)

1 Institute of Mathematics [Kosice, Slovakia]
2 ITI - Institut teoretické informatiky

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).

Mots clés: cubic graphs; random graphs; large girth; edge-cut

Domaines: Mathématique discrète [cs.DM]

František Kardoš, Daniel Kráľ, Jan Volec. Maximum edge-cuts in Cubic Graphs With Large Girth and in Random Cubic Graphs. Random Structures and Algorithms, 2012, 41 (4), pp.506-520. ⟨hal-00994798⟩