Name
Abstract | ||
|---|---|---|
An integral convex polytope P is said to be Gorenstein if its toric ring K[P] is normal and Gorenstein. In this paper, Gorenstein cut polytopes of graphs are characterized explicitly. First, we prove that Gorenstein cut polytopes are compressed (i.e., all of whose reverse lexicographic triangulations are unimodular). Second, by applying Athanasiadis's theory for Gorenstein compressed polytopes, we show that a cut polytope of a graph G is Gorenstein if and only if G has no K"5-minor and G is either a bipartite graph without induced cycles of length =6 or a bridgeless chordal graph. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.ejc.2013.11.010 | Eur. J. Comb. |
Keywords | DocType | Volume |
integral convex polytope,cut polytope,bipartite graph,gorenstein cut polytopes,toric ring k,graph g,reverse lexicographic triangulations,induced cycle,bridgeless chordal graph | Journal | 38, |
ISSN | Citations | PageRank |
European Journal of Combinatorics 38 (2014) 122--129 | 0 | 0.34 |
References | Authors | |
5 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hidefumi Ohsugi | 1 | 27 | 10.42 |