منابع مشابه
Locality of Connective Constants, Ii. Cayley Graphs
The connective constant μ(G) of an infinite transitive graph G is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimmett and Li, a locality theorem was proved for connective constants, namely, that the connective constants of two graphs are close in value whenever the graphs agree on a large ball around the origin. A condition of the th...
متن کاملLocality of Connective Constants, I. Transitive Graphs
The connective constant μ(G) of a quasi-transitive graph G is the exponential growth rate of the number of self-avoiding walks from a given origin. We prove a locality theorem for connective constants, namely, that the connective constants of two graphs are close in value whenever the graphs agree on a large ball around the origin. The proof exploits a generalized bridge decomposition of self-a...
متن کاملBounds on connective constants of regular graphs
Bounds are proved for the connective constant μ of an infinite, connected, ∆-regular graph G. The main result is that μ ≥ √ ∆− 1 if G is vertex-transitive and simple. This inequality is proved subject to weaker conditions under which it is sharp.
متن کاملSelf-avoiding Walks and Connective Constants
The connective constant μ(G) of a quasi-transitive graph G is the asymptotic growth rate of the number of selfavoiding walks (SAWs) on G from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph G. • We present upper and lower bounds for μ in terms of the vertex-degree and girth of a transitive graph. • We discuss the qu...
متن کاملStrict Inequalities for Connective Constants of Transitive Graphs
The connective constant of a graph is the exponential growth rate of the number of self-avoiding walks starting at a given vertex. Strict inequalities are proved for connective constants of vertex-transitive graphs. First, the connective constant decreases strictly when the graph is replaced by a nontrivial quotient graph. Second, the connective constant increases strictly when a quasitransitiv...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2018
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.08.013