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Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on Z^2
Uniform spanning tree loop-erased random walk abelian sandpile model
2011/9/14
Abstract: We show how to compute the probabilities of various connection topologies for uniformly random spanning trees on graphs embedded in surfaces. As an application, we show how to compute the "i...
Abstract: The boxicity of a graph $G=(V,E)$ is the smallest integer $k$ for which there exist $k$ interval graphs $G_i=(V,E_i)$, $1 \le i \le k$, such that $E=E_1 \cap...\cap E_k$. Scheinerman proved ...
Polynomial invariants of graphs on surfaces
Graphs on surfaces ribbon graphs matroids Krushkal polynomial
2011/2/25
For a graph embedded into a surface, we relate many combinatorial parameters of the cycle matroid of the graph and the bond matroid of the dual graph with the topological parameters of the embedding. ...