Cyclic timetabling for public transportation companies is usually modeled by the periodic event scheduling problem. To deduce a mixed-integer programming formulation, artificial integer variables have to be introduced. There are many ways to define these integer variables. We show that the minimal number of integer variables required to encode an instance is achieved by introducing an integer v...

A cycle packing in a (directed) multigraph is a vertex disjoint collection of (directed) elementary cycles. If D is a demiregular multidigraph we show that the arcs of D can be partitioned into Ai. cycle packings where Ain is the maximum indegree of a vertex in D. We then show that the maximum length cycle packings in any digraph contain a common vertex.

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 ...

We consider the problem of computing a minimum cycle basis in a directed graph G. The input to this problem is a directed graph whose arcs have positive weights. In this problem a 1 0 1 incidence vector is associated with each cycle and the vector space over generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. ...

Choosing a uniformly sampled simple directed graph realization of a degree sequence has many applications, in particular in social networks where self-loops are commonly not allowed. It has been shown in the past that one can perform a Markov chain arc-switching algorithm to sample a simple directed graph uniformly by performing two types of switches: a 2-switch and a directed 3-cycle reorienta...

Let T be a hamiltonian bipartite tournament with n vertices, γ a hamiltonian directed cycle of T , and k an even number. In this paper the following question is studied: What is the maximum intersection with γ of a directed cycle of length k contained in T [V (γ)]? It is proved that for an even k in the range n+6 2 ≤ k ≤ n−2, there exists a directed cycle Ch(k) of length h(k), h(k) ∈ {k, k − 2}...