Thursday, 14:15 - 14:40 h, Room: H 3004

 

Lamia Aoudia
4-cycle polytope on a graph

Coauthor: Meziane Aider

 

Abstract:
The aim of this work is to give a convex hull of 4-cycle on a wider class of complete bipartite graphs.\
Given a bipartite graph Kn,m, where |{V1}|=n and
|{V1}|=m, E=V1 × V2 and a weight function w: E → R, The minimum weighted 4-cycle problem consist on finding a 4-cycle C ⊂ E such hat e ∈ Cwe is minimum. This problem can easily be solved in polynomial time by complete enumeration of the the 4-cycles of G. For each 4-cycle C, let XC denote the incidence vector of C defined by: XC (e) = 1 and XC =0 if e\notin C. The 4-cycle polytope PC4 n , m is the convex hull of the incidence vectors of the 4-cycles of Kn,m, i.e. PC4 n , m = convex hull {XC ∈ {0,1}: C is a 4-cycle of G }
The minimum weighted 4-cycle problem is clearly equivalent to the linear program min {wx :  x ∈ PC4n,n }.
We are mainly interested by the facial tructure of PC4 n,m. Thus, we enumerate some inequalities defining facets of PC4 n, n.

 

Talk 3 of the contributed session Thu.2.H 3004
"Cycles in graphs" [...]
Cluster 2
"Combinatorial optimization" [...]

 

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