On the star forest polytope

Viet Hung Nguyen (1) , Lamia Aoudia (1) , A. Ridha Mahjoub , M. Aider

1 DECISION

A star forest is a collection of vertex-disjoint trees of depth at most 1, and its size is the number of leaves in all its components. A spanning star forest of a given graph G is a spanning subgraph of G that is also star forest. The spanning star forest problem (SSFP for short) [10] is to find maximum size spanning star forest of given graph. Let define some graph $G = (V;E)$, to every star forest we associate a vector $x^F . x^F (e) = 1$ if $e \in F$ and $x^F (e) = 0$ otherwise. $x^F$ is the incident vector of spanning star forest $F$. The convex hull of all spanning star forest incident vectors is called a spanning star forest polytope, denoted SFP(G). In this paper we are mainly interested on complete characterization of SFP(G).

Domaines: Informatique [cs]

Viet Hung Nguyen, Lamia Aoudia, A. Ridha Mahjoub, M. Aider. On the star forest polytope. International Conference on Control, Decision and Information Technologies (CoDIT), 2014, Nov 2014, Metz, France. pp.263-268, ⟨10.1109/CoDIT.2014.6996904⟩. ⟨hal-01213336⟩