Exact Solution of the Three-color Problem on a Random Lattice

Abstract

We present the exact solution of the Baxter's three-color problem on a random planar graph, using the random-matrix formulation of the problem, given by B. Eynard and C. Kristjansen. We find that the number of three-coloring of an infinite random graph is 0.9843 per vertex.

9 pages, 2 figures

References in corpus (4)

• D-particles, Matrix Integrals and KP hierachy
• Exact Solution of the Six-Vertex Model on a Random Lattice
• The six-vertex model on random lattices
• An Iterative Solution of the Three-colour Problem on a Random Lattice

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• Non-anomalous `Ward' identities to supplement large-N multi-matrix loop equations for correlations
• Formal matrix integrals and combinatorics of maps
• On gonihedric loops and quantum gravity
• Large-N Limit as a Classical Limit: Baryon in Two-Dimensional QCD and Multi-Matrix Models