YEO , Anders

Hoàng-Reed conjecture asserts that every digraph $D$ has a collection $\cal C$ of circuits $C_1,\dots,C_{\delta ^+}$, where $\delta ^+$ is the minimum outdegree of $D$, such that the circuits of $\cal C$ have a forest-like structure. Formally, $|V(C_i)\cap (V(C_1)\cup \dots \cup V(C_{i-1}))|\leq 1$, for all $i=2,\dots ,\delta^+$. We verify this...

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Hoàng-Reed conjecture asserts that every digraph $D$ has a collection $\cal C$ of circuits $C_1,\dots,C_{\delta ^+}$, where $\delta ^+$ is the minimum outdegree of $D$, such that the circuits of $\cal C$ have a forest-like structure. Formally, $|V(C_i)\cap (V(C_1)\cup \dots \cup V(C_{i-1}))|\leq 1$, for all $i=2,\dots ,\delta^+$. We verify this...

A digraph is eulerian if it is connected and every vertex has its in-degree equal to its outdegree. Having a spanning eulerian subdigraph is thus a weakening of having a hamiltonian cycle. In this paper, we first characterize the pairs (D, a) of a semicomplete digraph D and an arc a such that D has a spanning eulerian subdigraph containing a....

The concept of arc-disjoint flows in networks was recently introduced in \cite{bangTCSflow}. This is a very general framework within which many well-known and important problems can be formulated. In particular, the existence of arc-disjoint branching flows, that is, flows which send one unit of flow from a given source $s$ to all other...

A digraph is eulerian if it is connected and every vertex has its in-degree equal to its outdegree. Having a spanning eulerian subdigraph is thus a weakening of having a hamiltonian cycle. In this paper, we first characterize the pairs (D, a) of a semicomplete digraph D and an arc a such that D has a spanning eulerian subdigraph containing a....

The concept of arc-disjoint flows in networks was recently introduced in Bang-Jensen and Bessy (2014). This is a very general framework within which many well-known and important problems can be formulated. In particular, the existence of arc-disjoint branching flows, that is, flows which send one unit of flow from a given source s to all other...

For a given 2-partition (V1, V2) of the vertices of a (di)graph G, we study properties of the spanning bipartite subdigraph BG(V1, V2) of G induced by those arcs/edges that have one end in each Vi, i ∈ {1, 2}. We determine, for all pairs of non-negative integers k1, k2, the complexity of deciding whether G has a 2-partition (V1, V2) such that...

Let k be a fixed integer. We determine the complexity of finding a p-partition (V1,. .. , Vp) of the vertex set of a given digraph such that the maximum out-degree of each of the digraphs induced by Vi, (1 ≤ i ≤ p) is at least k smaller than the maximum out-degree of D. We show that this problem is polynomial-time solvable when p ≥ 2k and N...

We prove that every digraph of independence number at most 2 and arc-connectivity at least 2 has an out-branching $B+$ and an in-branching $B−$ which are arc-disjoint (we call such branchings a good pair). This is best possible in terms of the arc-connectivity as there are infinitely many strong digraphs with independence number 2 and...

An out-tree T is an oriented tree with only one vertex of in-degree zero. A vertex x of T is internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a given out-tree with k vertices. The algorithms are of running time O*(5.704k) and O*(6.14k), respectively. We...