The problem of orienting the edges an undirected graph such that resulting digraph is acyclic and has a single source s sink t long tradition in theory central to many drawing algorithms. Such orientation called st-orientation. We address computing st-orientations graphs with minimum number transitive edges. prove NP-hard general case. For planar we describe ILP model fast practice. experimenta...

In this paper, we investigate the computational complexity of subgraph reconfiguration problems in directed graphs. More specifically, focus on problem reconfiguring arborescences a digraph, where an arborescence is graph such that its underlying undirected forms tree and all vertices have in-degree at most 1. Given two goal to determine whether there (reconfiguration) sequence between given ea...

This paper gives a simple characterization of episodes in episode mining that are constructible from just information for occurrences of serial episodes, called serially constructible episodes. First, we formulate an episode as an acyclic transitive labeled digraph of which label is an event type in episode mining. Next, we introduce a parallel-free episode that always has an arc between vertic...

We present an algorithm for drawing directed graphs, which is based on rapidly solving a unique one-dimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can b...

The approach mapping from a matching of bipartite graphs to digraphs has been successfully used for forcing set problem, in this paper, it is extended to uniquely restricted matching problem. We show to determine a uniquely restricted matching in a bipartite graph is equivalent to recognition a acyclic digraph. Based on these results, it proves that determine the bipartite graphs with all maxim...

In this paper we initiate a systematic study of the Reduced Degree Spanning Tree problem, where given a digraph D and a nonnegative integer k, the goal is to construct a spanning out-tree with at most k vertices of reduced out-degree. This problem is a directed analog of the wellstudied Minimum-Vertex Feedback Edge Set problem. We show that this problem is fixed-parameter tractable and admits a...

For digraphs D and H , a mapping f : V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). For a fixed directed or undirected graph H and an input graph D, the problem of verifying whether there exists a homomorphism of D to H has been studied in a large number of papers. We study an optimization version of this decision problem. Our optimization problem is motivated by ...

A tournament T = (V,A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs whose removal results in an acyclic digraph. The Feedback Arc Set problem restricted to tournaments is known as the k-Feedback Arc Set in Tou...

We propose to study a problem that arises naturally from both Topological Numbering of Directed Acyclic Graphs, and Additive Coloring (also known as Lucky Labeling). Let D be a digraph and f a labeling of its vertices with positive integers; denote by S(v) the sum of labels over all neighbors of each vertex v. The labeling f is called topological additive numbering if S(u) < S(v) for each arc (...

Graphs and digraphs in this paper may have loops and multiple edges. Paths and circuits have no “repeated” vertices, and in digraphs they are directed. A transversal in a digraph D is a set of vertices T which intersects every circuit, i.e. DnT is acyclic. A packing of circuits (or packing for short) is a collection of pairwise (vertex-)disjoint circuits. The cardinality of a minimum transversa...