Covering a cubic graph with perfect matchings
نویسندگان
چکیده
منابع مشابه
Covering a cubic graph by 5 perfect matchings
Berge Conjecture states that every bridgeless cubic graph has 5 perfect matchings such that each edge is contained in at least one of them. In this paper, we show that Berge Conjecture holds for two classes of cubic graphs, cubic graphs with a circuit missing only one vertex and bridgeless cubic graphs with a 2-factor consisting of two circuits. The first part of this result implies that Berge ...
متن کاملperfect matchings in edge-transitive graph
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...
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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.06.006