we present a matching and lp based heuristic algorithm that decides graph non-hamiltonicity. each of the n! hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices p, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. a graph instance (g) is initially coded as exclusion set ...

One method for counting weighted cycle systems in a graph entails taking the determinant of the identity matrix minus the adjacency matrix of the graph. The result of this operation is the sum over cycle systems of −1 to the power of the number of disjoint cycles times the weight of the cycle system. We use this fact to reprove that the determinant of a matrix of much smaller order can be compu...

This paper deals with hub-and-spoke network design in the liner shipping sector. It introduces a capacitated directed cycle hub location and cargo routing problem under congestion. The involves four decisions: of ports; allocation non-hub ports to construction cyclic route at port level; between all origin-destination demand pairs network. objective is minimize cost which includes fixed opening...

A directed odd cycle transversal of a directed graph (digraph) D is a vertex set S that intersects every odd directed cycle of D. In the Directed Odd Cycle Transversal (DOCT) problem, the input consists of a digraph D and an integer k. The objective is to determine whether there exists a directed odd cycle transversal of D of size at most k. In this paper, we settle the parameterized complexity...

The even cycle problem for both undirected [Tho88] and directed [RST99] graphs has been the topic of intense research in the last decade. In this paper, we study the computational complexity of cycle length modularity problems. Roughly speaking, in a cycle length modularity problem, given an input (undirected or directed) graph, one has to determine whether the graph has a cycle C of a specific...

Let G = (V, E) be a digraph (i.e., a directed graph) with n vertices and m edges, and w : E → IR be a weight function on the edges. A directed cycle is closed walkC = (v0, v1, . . . , vt), where vt = v0 and (vi → vi+1) ∈ E, for i = 0, . . . , t − 1. The average cost of a directed cycle is AvgCost(C) = ω(C)/t = (∑e∈C ω(e)) /t. For each k = 0, 1, . . ., and v ∈ V , let dk(v) denote the minimum le...