01/04/2025    15:00 > "Total Matching and Subdeterminants". 

Yelena Yuditski (ULB) 

will give a presentation on : 

Total Matching and Subdeterminants. 

Abstract : 

In the total matching problem, one is given a graph G with weights on the vertices and edges. The goal is to find a maximum weight set of vertices and edges that is the non-incident union of a stable set and a matching. We consider the natural formulation of the problem as an integer program (IP), with variables corresponding to vertices and edges. Let M = M(G) denote the constraint matrix of this IP. We define Delta(G) as the maximum absolute value of the determinant of a square submatrix of M. We show that the total matching problem can be solved in strongly polynomial time provided Delta(G) <= Delta for some constant Delta is an element of Z(>= 1). We also show that the problem of computing Delta(G) admits an FPT algorithm. We also establish further results on Delta(G) when G is a forest. 

   CORE B.-135