منابع مشابه
Perfect matchings in planar cubic graphs
A well-known conjecture of Lovász and Plummer from the mid-1970’s, still open, asserts that for every cubic graph G with no cutedge, the number of perfect matchings in G is exponential in |V (G)|. In this paper we prove the conjecture for planar graphs; we prove that if G is a planar cubic graph with no cutedge, then G has at least 2 (G)|/655978752
متن کاملNon-intersecting perfect matchings in cubic graphs
A conjecture of G. Fan and A. Raspaud asserts that every bridgeless cubic graph contains three perfect matchings with empty intersection. We suggest a possible approach to problems of this type, based on the concept of a balanced join in an embedded graph. We use this method to prove a special case of a conjecture of E. Máčajová and M. Škoviera on Fano colorings of cubic graphs.
متن کاملUnions of perfect matchings in cubic graphs
We show that any cubic bridgeless graph with m edges contains two perfect matchings that cover at least 3m/5 edges, and three perfect matchings that cover at least 27m/35 edges.
متن کاملPerfect Matchings in Claw-free Cubic Graphs
Lovász and Plummer conjectured that there exist a fixed positive constant c such that every cubic n-vertex graph with no cutedge has at least 2cn perfect matchings. Their conjecture has been verified for bipartite graphs by Voorhoeve and planar graphs by Chudnovsky and Seymour. We prove that every claw-free cubic n-vertex graph with no cutedge has more than
متن کاملPerfect Matchings in Edge-Transitive Graphs
We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2012
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-012-2660-9