66 citations · 468 across the 34 of their papers we have counts for
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math.CO2009★ 38 cited
The number of extreme points of tropical polyhedra
Xavier Allamigeon, Stephane Gaubert, Ricardo D. Katz
The celebrated upper bound theorem of McMullen determines the maximal number of extreme points of a polyhedron in terms of its dimension and the number of constraints which define…
math.CO2009★ 54 cited
Computing the vertices of tropical polyhedra using directed hypergraphs
Xavier Allamigeon, Stephane Gaubert, Eric Goubault
We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if,…