Hypergraph multiway cut problem is a problem of finding a minimum capacity set of hyperedges whose removal divides a given hypergraph into a specified number of connected components. We present an algorithm for this problem which runs in strongly polynomial-time if both the specified number of connected components and the maximum size of hyperedges in the hypergraph are constants. Our algorithm...

An arena is a finite directed graph whose vertices are divided into two classes, i.e., V = V ∪ V#; this forms the basic playground for a plethora of 2-player infinite pebble-games. We introduce and study a refined notion of reachability for arenas, named trap-reachability, where Player attempts to reach vertices without leaving a prescribed subset V ′ ⊆ V , while Player # works against. It is s...

The computation of the strongly connected components of a directed graph is one of the fundamental algorithmic graph problems. Linear-time algorithms with simple implementations are known. Here a simplified correctness proof for one of these algorithms is presented.

For a directed graph D = (V,E), a Strongly Connected Component (SCC) is a maximal induced subgraph S = (VS , ES) where, for every x, y ∈ VS , there is a path from x to y (and vice-versa). Tarjan presented a now well-established algorithm for computing the strongly connected components of a digraph in time Θ(v+e) [8]. In the worst case, this needs v(2 + 5w) bits of storage, where w is the machin...

In this paper, we study the density of fixed strongly connected subtournaments on 5 vertices in large tournaments. We determine the maximum density asymptotically for three tournaments as well as extremal families for each tournament. We use Razborov’s semidefinite method for flag algebras to prove the upper bounds.

In argumentation theory, Dung’s abstract framework provides a unifying view of several alternative semantics based on the notion of extension. Recently, a new semantics has been introduced to solve the problems related to counterintuitive results produced by literature proposals. In this semantics, extensions can be decomposed and constructed along the strongly connected components of the defea...

Rival and Zaguia showed that the antichain cutsets of a finite Boolean lattice are exactly the level sets. We show that a similar characterization of antichain cutsets holds for any strongly connected poset of locally finite height. As a corollary, we characterize the antichain cutsets in semimodular lattices, supersolvable lattices, Bruhat orders, locally shellable lattices, and many more. We ...

Article history: Received 1 October 2012 Received in revised form 9 February 2015 Accepted 10 February 2015 Available online 14 February 2015