Percolation on Finite Cayley Graphs

نویسندگان

  • Christopher Malon
  • Igor Pak
چکیده

In this paper, we study percolation on finite Cayley graphs. A conjecture of Benjamini says that the critical percolation pc of any vertex–transitive graph satisfying a certain diameter condition can be bounded away from one. We prove Benjamini’s conjecture for some special classes of Cayley graphs. We also establish a reduction theorem, which allows us to build Cayley graphs for large groups without increasing pc.

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

On the Finite Groups that all Their Semi-Cayley Graphs are Quasi-Abelian

In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.

متن کامل

Critical percolation on Cayley graphs of groups acting on trees

This article presents a method for finding the critical probability pc for the Bernoulli bond percolation on graphs with the so called tree-like structure. Such graphs can be decomposed into a tree of pieces which have finitely many isomorphism classes. This class of graphs includes the Cayley graphs of amalgamated products, HNN extensions or general groups acting on trees. It also includes all...

متن کامل

NORMAL 6-VALENT CAYLEY GRAPHS OF ABELIAN GROUPS

Abstract : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6 was presented.  

متن کامل

ov 2 00 7 Cutsets in infinite graphs by Ádám Timár

We answer three questions posed in a paper by Babson and Benjamini. They introduced a parameter CG for Cayley graphs G that has significant application to percolation. For a minimal cutset of G and a partition of this cutset into two classes, take the minimal distance between the two classes. The supremum of this number over all minimal cutsets and all partitions is CG. We show that if it is fi...

متن کامل

Non - Amenable Cayley Graphs of High Girth

In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., pc < pu . Furthermore, we show that percolation and self-avoiding walk on such graphs have mean-field critical exponents. In particular, the self-avoiding walk has positive speed.

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:
  • Combinatorics, Probability & Computing

دوره 15  شماره 

صفحات  -

تاریخ انتشار 2002