Separating hyperplanes of edge polytopes

Details Separating hyperplanes of edge polytopes Separating hyperplanes of edge polytopes

2011-12-21

arxiv.org/abs/1112.5047v1

Mathematics

Combinatorics

15pages

Scientific paper

Let $G$ be a finite connected simple graph with $d$ vertices and let $\Pc_G \subset \RR^d$ be the edge polytope of $G$ . We call $\Pc_G$ \emph{decomposable} if $\Pc_G$ decomposes into integral polytopes $\Pc_{G^+}$ and $\Pc_{G^-}$ via ae hyperplane, and we give an algorithm which determines the decomposability of an edge polytope. We prove that when $\Pc_G$ is decomposable, $\Pc_G$ is normal if and only if both $\Pc_{G^+}$ and $\Pc_{G^-}$ are normal. We also study toric ideals of $\Pc_{G}, \Pc_{G^+}$ and $\Pc_{G^-}$.

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