Graphs, Morphisms, and Statistical Physics: DIMACS Workshop Graphs, Morphisms and Statistical Physics, March 19-21, 2001, DIMACS Center
Jaroslav Nešetřil, Peter Winkler
American Mathematical Soc. - Science - 193 pages
The intersection of combinatorics and statistical physics has experienced great activity in recent years. This flurry of activity has been fertilized by an exchange not only of techniques, but also of objectives. Computer scientists interested in approximation algorithms have helped statistical physicists and discrete mathematicians overcome language problems. They have found a wealth of common ground in probabilistic combinatorics. Close connections between percolation and random graphs, graph morphisms and hard-constraint models, and slow mixing and phase transition have led to new results and perspectives. These connections can help in understanding typical behavior of combinatorial phenomena such as graph coloring and homomorphisms. Inspired by issues and intriguing new questions surrounding the interplay of combinatorics and statistical physics, a DIMACS/DIMATIA workshop was held at Rutgers University. These proceedings are the outgrowth of that meeting. This volume is intended for graduate students and research mathematicians interested in probabilistic graph theory and its applications.
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Efficient Local Search near Phase Transitions in Combinatorial Optimization
on the Hypercubic Lattice
Graph Homomorphisms and Long Range Action
Random Walks and Graph Homomorphisms
Recent results on Parameterized HColoring
Rapidly mixing Markov chains for dismantleable constraint graphs
On weighted graph homomorphisms
Counting List Homomorphisms for Graphs with Bounded Degrees
On the satisfiability of random kHorn formulae
The exchange interaction spin hamiltonians and the symmetric group
A Discrete NonPfaffian Approach to the Ising Problem
Information flow on trees
Fractional aspects of Hedetniemis conjecture
Perfect graphs for generalized colouring circular perfect graphs
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adjacent algorithm assume bipartite graph Brightwell circular perfect clauses coloring of G coloring problem combinatorial complete bipartite graph complete graph component condition configuration conjecture consider constraint graph contains contours Corollary corresponding counting the number defined denote digraph directed graph dismantlable Dyer edge Editors exists finite formula function G to H Gibbs measures given Glauber dynamics graph G graph homomorphisms H-coloring hamiltonian hence Hom(G HORN-SAT implies independent set induced path input graph irreflexive Ising model label Lemma Let G list coloring list homomorphisms long range action loop Markov chains Math Mathematics mean-field approximation Nesetfil node non-periodic closed walks NP-complete obtained Optimization parameterized partial weighted assignment partition phase transition polynomial Potts models probability proof of Theorem prove random walk reconstruction problem satisfies spin glass stationary distribution statistical physics subset Theorem 2.1 theory tree decomposition treewidth variables vertex of Ax vertices well-linked with respect Winkler
Page 85 - P. Hell, J. Nesetfil, and X. Zhu, Duality and polynomial testing of tree homomorphisms, Trans. Amer. Math. Soc.