GARNERO , Valentin

By Berge's theorem, finding a maximum matching in a graph relies on the use of augmenting paths. When no further constraint is added, Edmonds' algorithm allows to compute a maximum matching in polynomial time by sequentially augmenting such paths. Motivated by applications in the scheduling of airline operations, we consider a similar problem...

Due to a classical result of Berge, it is known that a matching of any graph can be turned into a maximum matching by repeatedly augmenting alternating paths whose ends are not covered. In a recent work, Nisse, Salch and Weber considered the influence, on this process, of augmenting paths with length at most k only. Given a graph G, an initial...

Due to a classical result of Berge, it is known that a matching of any graph can be turned into a maximum matching by repeatedly augmenting alternating paths whose ends are not covered. In a recent work, Nisse, Salch and Weber considered the influence, on this process, of augmenting paths with length at most k only. Given a graph G, an initial...

During the last years, several algorithmic meta-theorems have appeared (Bodlaender et al. [FOCS 2009], Fomin et al. [SODA 2010], Kim et al. [ICALP 2013]) guaranteeing the existence of linear kernels on sparse graphs for problems satisfying some generic conditions. The drawback of such general results is that it is usually not clear how to...