Name
Abstract | ||
|---|---|---|
Let Gn be the complete graph on the vertex set [n] = {1, 2, ..., n} and ω an orientation of Gn, i,e., ω is an assignment of a direction i → j of each edge {i, j} of Gn. Let eq denote the qth unit coordinate vector of Rn. Write P(Gn;ω) ⊂ Rn for the convex hull of the (n 2) points ei - ej, where i → j is the direction of the edge {i, j} in the orientation ω. It will be proved that, for n ≥ 5, the Ehrhart ring of the convex polytope P(Gn;ω) is Gorenstein if and only if (Gn;ω) possesses a Hamiltonian cycle, i.e., a directed cycle of length n. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1006/eujc.2002.0572 | Eur. J. Comb. |
Keywords | Field | DocType |
complete graph,ehrhart ring,convex hull,write p,eq denote,convex polytope,gorenstein ring,direction i,hamiltonian tournament,points ei,length n,hamiltonian cycle | Coordinate vector,Discrete mathematics,Complete graph,Combinatorics,Vertex (geometry),Hamiltonian (quantum mechanics),Hamiltonian path,Convex hull,Regular polygon,Mathematics | Journal |
Volume | Issue | ISSN |
23 | 4 | 0195-6698 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hidefumi Ohsugi | 1 | 27 | 10.42 |
| Takayuki Hibi | 2 | 94 | 30.08 |