Graphs, Morphisms, and Statistical Physics: DIMACS Workshop Graphs, Morphisms and Statistical Physics, March 19-21, 2001, DIMACS CenterJaroslav Nešetřil, Peter Winkler 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. |
Contents
Efficient Local Search near Phase Transitions in Combinatorial Optimization | 1 |
on the Hypercubic Lattice | 13 |
Graph Homomorphisms and Long Range Action | 29 |
Random Walks and Graph Homomorphisms | 49 |
Recent results on Parameterized HColoring | 65 |
Rapidly mixing Markov chains for dismantleable constraint graphs | 87 |
On weighted graph homomorphisms | 97 |
Counting List Homomorphisms for Graphs with Bounded Degrees | 105 |
On the satisfiability of random kHorn formulae | 113 |
The exchange interaction spin hamiltonians and the symmetric group | 137 |
A Discrete NonPfaffian Approach to the Ising Problem | 145 |
Information flow on trees | 155 |
Fractional aspects of Hedetniemis conjecture | 171 |
Perfect graphs for generalized colouring circular perfect graphs | 177 |
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Common terms and phrases
a₁ adjacent algorithm assume bipartite graph bounded clauses color combinatorial complete bipartite graph complete graph component condition configuration conjecture connected consider constraint graph contains contours COROLLARY corresponding counting the number defined degree denote digraph directed graph dismantlable edge exists finite formula function G to H Gibbs measures given Glauber dynamics graph G graph homomorphisms H-coloring of G H-coloring problem hamiltonian hence Hom(G Hom(Td HORN-SAT implies independent set induced path input graph irreflexive Ising model K)-coloring Kk/d label Lemma list H list H-coloring list homomorphisms long range action loop Markov chains Math Mathematics maximum vertex Nešetřil node non-periodic closed walks NP-complete obtained optimization parameterized partial weighted assignment partition phase transition Phys polynomial Potts models probability prove random walk reconstruction problem satisfies spin glass stationary distribution statistical physics subset symmetric Theorem 2.1 tree decomposition treewidth variables vertices Winkler