Unions of perfect matchings in cubic graphs
نویسندگان
چکیده
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.
منابع مشابه
Perfect 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...
متن کاملUnions of Perfect Matchings in Cubic Graphs and Implications of the Berge-Fulkerson Conjecture
The Berge-Fulkerson Conjecture states that every cubic bridgeless graph has six perfect matchings such that every edge of the graph is in exactly two of the perfect matchings. If the Berge-Fulkerson Conjecture is true, then what can we say about the proportion of edges of a cubic bridgeless graph that can be covered by k of its perfect matchings? This is the question we address in this paper. W...
متن کاملA New Lower Bound on the Number of Perfect Matchings in Cubic Graphs
We prove that every n-vertex cubic bridgeless graph has at least n/2 perfect matchings and give a list of all 17 such graphs that have less than n/2 + 2 perfect matchings.
متن کاملCovering 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 کاملOn the perfect matching index of bridgeless cubic graphs
If G is a bridgeless cubic graph, Fulkerson conjectured that we can find 6 perfect matchings M1, . . . ,M6 of G with the property that every edge of G is contained in exactly two of them and Berge conjectured that its edge set can be covered by 5 perfect matchings. We define τ(G) as the least number of perfect matchings allowing to cover the edge set of a bridgeless cubic graph and we study thi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 22 شماره
صفحات -
تاریخ انتشار 2005