Perfect matchings in planar cubic graphs

نویسندگان

  • Maria Chudnovsky
  • Paul D. Seymour
چکیده

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

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Perfect 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 کامل

A 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 کامل

A bound on the number of perfect matchings in Klee-graphs

We focus on a specific class of planar cubic bridgeless graphs, namely the klee-graphs. K4 is the smallest klee-graph and having a klee-graph G we create another klee-graph by replacing any vertex of G by a triangle, i.e., applying Y∆ operation. In this paper, we prove that every klee-graph with n ≥ 8 vertices has at least 3 · 2 perfect matchings, improving the 2 bound inherited from the genera...

متن کامل

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 کامل

Counting perfect matchings of cubic graphs in the geometric dual

Lovász and Plummer conjectured, in the mid 1970’s, that every cubic graph G with no cutedge has an exponential in |V (G)| number of perfect matchings. In this work we show that every cubic planar graph G whose geometric dual graph is a stack triangulation has at least 3φ (G)|/72 distinct perfect matchings, where φ is the golden ratio. Our work builds on a novel approach relating Lovász and Plum...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Combinatorica

دوره 32  شماره 

صفحات  -

تاریخ انتشار 2012