4 papers · 1 filter
Quasi-kernels in split graphs
Hélène Langlois, Frédéric Meunier, Romeo Rizzi +2
In a digraph, a quasi-kernel is a subset of vertices that is independent and such that the shortest path from every vertex to this subset is of length at most two. The ``small quas…
Note on Disjoint Cycles in Multipartite Tournaments
Gregory Gutin, Wei Li, Shujing Wang +2
In 1981, Bermond and Thomassen conjectured that for any positive integer , every digraph with minimum out-degree at least admits vertex-disjoint directed cycles. In t…
On Seymour's and Sullivan's Second Neighbourhood Conjectures
Jiangdong Ai, Stefanie Gerke, Gregory Gutin +3
For a vertex of a digraph, (, resp.) is the number of vertices at distance 1 from (to, resp.) and is the number of vertices at distance 2 from…
Bounds on Maximum Weight Directed Cut
Jiangdong Ai, Stefanie Gerke, Gregory Gutin +2
We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses.…