Ideals of Graph Homomorphisms release_ozaoxmwhl5hhrapqrckfu52x6u

by Alexander Engstrom, Patrik Noren

Released as a article .

2011  

Abstract

In combinatorial commutative algebra and algebraic statistics many toric ideals are constructed from graphs. Keeping the categorical structure of graphs in mind we give previous results a more functorial context and generalize them by introducing the ideals of graph homomorphisms. For this new class of ideals we investigate how the topology of the graphs influence the algebraic properties. We describe explicit Grobner bases for several classes, generalizing results by Hibi, Sturmfels and Sullivant. One of our main tools is the toric fiber product, and we employ results by Engstrom, Kahle and Sullivant. The lattice polytopes defined by our ideals include important classes in optimization theory, as the stable set polytopes.
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Type  article
Stage   submitted
Date   2011-09-07
Version   v4
Language   en ?
arXiv  1002.4679v4
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