Isaak posed the following problem. Suppose T is a tournament having a minimum feedback arc set which induces an acyclic digraph with a hamiltonian path. Is it true that the maximum number of arc-disjoint cycles in T equals the cardinality of minimum feedback arc set of T? We prove that the answer to the problem is in the negative. Further, we study the number of arc-disjoint cycles through a ve...

In this paper, we formulate an episode in episode mining as an acyclic transitive labeled digraph. Also we introduce an elliptic episode s → [S1, . . . , Sn] → t such that s and t are event types, [S1, . . . , Sn] is a sequence of serial episodes, and every pair of Si and Sj shares no same event type. Then, we show that every elliptic episode is constructible from serial episodes. Next, in this...

Consider the problem of finding a large induced acyclic subgraph of a given simple digraph D = (V,E). The decision version of this problem is NP -complete and its optimization is not likely to be approximable within a ratio of O(n ) for some > 0. We study this problem when D is a random instance. We show that, almost surely, any maximal solution is within an o(ln n) factor from the optimal one....

A digraph that represents reasonably a scheduling problem should have no cycles i.e. it should be DAG i.e. a directed acyclic graph. Here down we shall deal with special kind of graded DAGs named KoDAGs. For their definition and first primary properties see [1], where natural join of di-bigraphs (directed bi-parted graphs) and their corresponding adjacency matrices is defined and then applied t...

Given a stochastic, acyclic, connected digraph with a single source node and a control agent that repetitively traverses this graph, each time starting from the source node, we want to define a control policy that will enable this agent to visit each of the graph terminal nodes a prespecified number of times, while minimizing the expected number of the graph traversals. We formulate this proble...

A composite object represented as a directed graph (digraph for short) is an important data structure that requires efficient support in CAD/CAM, CASE, office systems, software management, web databases, and document databases. It is cumbersome to handle such objects in relational database systems when they involve ancestor-descendant relationships (or say, recursive relationships). In this pap...

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...

William F. Klostermeyer Dept. Statistics and Computer Science West Virginia University Morgantown, WV 26506-6330 e-mail: [email protected] ABSTRACT A directed graph operation called pushing a vertex is studied. When a vertex is pushed, the orientation of each of its incident edges is reversed. We consider the problems of pushing vertices so as to produce strongly connected, semi-connected, and acy...

Given a weighted directed graph G = (V,A), the minimum feedback arc set problem consists of finding a minimum weight set of arcs A ⊆ A such that the directed graph (V,A \ A) is acyclic. Similarly, the minimum feedback vertex set problem consists of finding a minimum weight set of vertices containing at least one vertex for each directed cycle. Both problems are NP-complete. We present simple co...

It is known (Bollobás [4]; Kostochka and Mazurova [13]) that there exist graphs of maximum degree ∆ and of arbitrarily large girth whose chromatic number is at least c∆/ log ∆. We show an analogous result for digraphs where the chromatic number of a digraph D is defined as the minimum integer k so that V (D) can be partitioned into k acyclic sets, and the girth is the length of the shortest cyc...