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Article Dans Une Revue International Transactions in Operational Research Année : 2001

On the linear description of the k-cycle polytope

Viet Hung Nguyen
Jean-François Maurras
  • Fonction : Auteur

Résumé

We study a linear description of $PC^k_n$ the convex hull of incidence vectors of all the cycles consisting of exactly $k$ edges ($k \ge 4$) in $K_n$, the complete undirected graph with $n$ vertices. First, we describe some properties of $PC^k_n$. Second, we discuss relations between $PC^k_n$ and $PC^{k'}_{n'}$ with $k' > k$ and $n' > n$. Then we give three lifting algorithms that transform a facet of $PC^k_n$ into facets of $PC^k_{n'}$ with $n' > n$. Finally, we provide an integer formulation and a partial linear description of $PC^k_n$.

Dates et versions

hal-01149566 , version 1 (07-05-2015)

Identifiants

Citer

Viet Hung Nguyen, Jean-François Maurras. On the linear description of the k-cycle polytope. International Transactions in Operational Research, 2001, 8 (6), pp.673-692. ⟨10.1111/1475-3995.t01-1-00331⟩. ⟨hal-01149566⟩
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