‎an  oriented perfect path double cover (oppdc) of a‎ ‎graph $g$ is a collection of directed paths in the symmetric‎ ‎orientation $g_s$ of‎ ‎$g$ such that‎ ‎each arc‎ ‎of $g_s$ lies in exactly one of the paths and each‎ ‎vertex of $g$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎maxov{'a} and ne{v{s}}et{v{r}}il (discrete‎ ‎math‎. ‎276 (2004) 287-294) conjectured that ...

a compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. directed hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. sets of extrema of birkhoff polyhedra are mapped to tours ...

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

Abstract. Many formal method tools for increasing software reliability apply Satisfiability Modulo Theories (SMT) solvers to enumerate feasible paths in a program subject to certain coverage criteria. Examples include inconsistent code detection tools and concolic test case generators. These tools have in common that they typically treat the SMT solver as a black box, relying on its ability to ...

Definitions of graph embeddings and graph minors for directed graphs are introduced. For the class of 2-terminal directed acyclic graphs (TDAGs) the definitions coincide, and the class is closed under both operations. The usefulness of the directed embedding operation is demonstrated be characterizing all TDAGs with parallel-width at most $k$, which generalizes earlier characterizations of seri...

We study the problem of exploring all nodes of an unknown directed graph. A searcher has to construct a tour that visits all nodes, but only has information about the parts of the graph it already visited. The goal is to minimize the cost of such a tour. In this paper, we present upper and lower bounds for both the deterministic and the randomized online version of exploring all nodes of direct...

In this paper, we propose the Directed Graph Embedding (DGE) method that embeds vertices on a directed graph into a vector space by considering the link structure of graphs. The basic idea is to preserve the locality property of vertices on a directed graph in the embedded space. We use the transition probability together with the stationary distribution of Markov random walks to measure such l...