Strict Inequalities for Connective Constants of Transitive Graphs

DOI10.1137/130906052zbMath1305.05102arXiv1301.3091OpenAlexW1972283381MaRDI QIDQ2935271

Zhongyang Li, Geoffrey R. Grimmett

Publication date: 22 December 2014

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.3091

zbMATH Keywords

Cayley graphregular graphvertex-transitive graphself-avoiding walkquasi-transitive graphconnective constant

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Enumeration in graph theory (05C30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (11)

Connective constants and height functions for Cayley graphs ⋮ Self-avoiding walks and amenability ⋮ Strict monotonicity of percolation thresholds under covering maps ⋮ A Note on Schramm’s Locality Conjecture for Random-Cluster Models ⋮ Self-Avoiding Walks and Connective Constants ⋮ Bounds on connective constants of regular graphs ⋮ Cubic graphs and the golden mean ⋮ Self-avoiding walk on nonunimodular transitive graphs ⋮ Counting self-avoiding walks on free products of graphs ⋮ Locality of connective constants ⋮ Positive speed self-avoiding walks on graphs with more than one end

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