4 We prove that the weak k-linkage problem is polynomial for every fixed k for totally Φ5 decomposable digraphs, under appropriate hypothesis on Φ. We then apply this and recent results 6 by Fradkin and Seymour (on the weak k-linkage problem for digraphs of bounded independence 7 number or bounded cut-width) to get polynomial algorithms for some class of digraphs like quasi8 transitive digraphs...

it has been proved that sphericity testing for digraphs is an np-complete problem. here, we investigate sphericity of 3-connected single source digraphs. we provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $o(n)$ time.

We study digraphs preserved by a Maltsev operation: Maltsev digraphs. We show that these digraphs retract either onto a directed path or to the disjoint union of directed cycles, showing in this way that the constraint satisfaction problem for Maltsev digraphs is in logspace, L. We then generalize results from Kazda (2011) to show that a Maltsev digraph is preserved not only by a majority opera...

Two problems of Cameron, Praeger, and Wormald [Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica (1993)] are resolved. First, locally finite highly arc-transitive digraphs with universal reachability relation are presented. Second, constructions of two-ended highly arc-transitive digraphs are provided, where each ‘building block’ is a finite bipartite digrap...

We use an exhaustive generation with isomorph-rejection to classify three types of structured digraphs. The first type is the class of regular digraphs where each vertex has the same number of out-neighbors and inneighbors. The second type is the class of normally regular digraphs introduced by Jørgensen. In these digraphs, the number of common out-neighbors (or inneighbors) of vertices x and y...

We consider digraphs – called extended locally semicomplete digraphs, or extended LSD’s, for short – that can be obtained from locally semicomplete digraphs by substituting independent sets for vertices. We characterize Hamiltonian extended LSD’s as well as extended LSD’s containing Hamiltonian paths. These results as well as some additional ones imply polynomial algorithms for finding a longes...

The Moore bound for a diregular digraph of degree d and diameter k is Md k d d It is known that digraphs of order Md k do not exist for d and k or In this paper we study digraphs of degree d diameter k and order Md k denoted by d k digraphs Miller and Fris showed that k digraphs do not exist for k Subsequently we gave a necessary condition of the existence of k digraphs namely k digraphs do not...

Containment and overlap representations of digraphs are studied, with the following results. The interval containment digraphs are the digraphs of Ferrers dimension 2, and the circular-arc containment digraphs are the complements of circular-arc intersection digraphs. A poset is an interval containment poset if and only if its comparability digraph is an interval containment digraph, and a grap...

By using biclique partitions of digraphs, this paper gives reduction formulas for the number oriented spanning trees, stationary distribution vector and Kemeny's constant digraphs. As applications, we give a method enumerating trees undirected graphs by vertex degrees partitions. The partition formula also extends results Knuth Levine from line digraphs to general