On the perfect matching index of bridgeless cubic graphs
نویسندگان
چکیده
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 this parameter. The set of graphs with perfect matching index 4 seems interesting and we give some informations on this class.
منابع مشابه
A note on Fouquet-Vanherpe’s question and Fulkerson conjecture
The excessive index of a bridgeless cubic graph $G$ is the least integer $k$, such that $G$ can be covered by $k$ perfect matchings. An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless cubic graph has excessive index at most five. Clearly, Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5, so Fouquet and Vanherpe as...
متن کاملOn Cubic Bridgeless Graphs Whose Edge-Set Cannot be Covered by Four Perfect Matchings
The problem of establishing the number of perfect matchings necessary to cover the edge-set of a cubic bridgeless graph is strictly related to a famous conjecture of Berge and Fulkerson. In this paper we prove that deciding whether this number is at most 4 for a given cubic bridgeless graph is NP-complete. We also construct an infinite family F of snarks (cyclically 4-edge-connected cubic graph...
متن کاملA superlinear bound on the number of perfect matchings in cubic bridgeless graphs
Lovász and Plummer conjectured in the 1970’s that cubic bridgeless graphs have exponentially many perfect matchings. This conjecture has been verified for bipartite graphs by Voorhoeve in 1979, and for planar graphs by Chudnovsky and Seymour in 2008, but in general only linear bounds are known. In this paper, we provide the first superlinear bound in the general case.
متن کاملPerfect matching covering, the Berge-Fulkerson conjecture, and the Fan-Raspaud conjecture
Let m∗t be the largest rational number such that every bridgeless cubic graph G associated with a positiveweightω has t perfectmatchings {M1, . . . ,Mt}withω(∪i=1 Mi) ≥ m ∗ t ω(G). It is conjectured in this paper that m∗3 = 4 5 , m ∗ 4 = 14 15 , and m ∗ 5 = 1, which are called the weighted PM-covering conjectures. The counterparts of this new invariant m∗t and conjectures for unweighted cubic g...
متن کاملThe Cost of Perfection for Matchings in Graphs
Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the application in triangle meshes, where we seek to convert a triangulation into a quadrangulation by merging pairs of adjacent triangles, we focus on bridgeless cubic graph...
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:
- CoRR
دوره abs/0904.1296 شماره
صفحات -
تاریخ انتشار 1971