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math.CO2010
Chip-Firing and Riemann-Roch Theory for Directed Graphs
Arash Asadi, Spencer Backman
We investigate Riemann-Roch theory for directed graphs. The Riemann-Roch criteria of Amini and Manjunath is generalized to all integer lattices orthogonal to some positive vector.…
math.CO2010
Sub-exponentially many 3-colorings of triangle-free planar graphs
Arash Asadi, Zdenek Dvorak, Luke Postle +1
Thomassen conjectured that every triangle-free planar graph on n vertices has exponentially many 3-colorings, and proved that it has at least 2^[n^(1/12)/20000] distinct 3-coloring…