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cond-mat.stat-mech2003★ 23 cited
Statistics of planar graphs viewed from a vertex: A study via labeled trees
J. Bouttier, P. Di Francesco, E. Guitter
We study the statistics of edges and vertices in the vicinity of a reference vertex (origin) within random planar quadrangulations and Eulerian triangulations. Exact generating fun…
cond-mat.stat-mech2003★ 163 cited
Geodesic Distance in Planar Graphs
J. Bouttier, P. Di Francesco, E. Guitter
We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This…