Consider the random graph process where we start with an empty graph on n vertices, and at time t, are given an edge et chosen uniformly at random among the edges which have not appeared so far. A classical result in random graph theory asserts that whp the graph becomes Hamiltonian at time (1/2+o(1))n log n. On the contrary, if all the edges were directed randomly, then the graph has a directe...

Jaeger’s directed cycle double cover conjecture can be formulated as a problem of existence of special perfect matchings in a class of graphs that we call hexagon graphs. In this work, we explore the structure of hexagon graphs. We show that hexagon graphs are braces that can be generated from the ladder on 8 vertices using two types of McCuaig’s augmentations.

We examine the necessary and sufficient conditions for a complete symmetric digraph K n to admit a resolvable decomposition into directed cycles of length m. We give a complete solution for even m, and a partial solution for odd m.

In this paper, we introduce an O(nm) time algorithm to determine the minimum length directed cycle in a directed network with n nodes and m arcs and with no negative length directed cycles. This result improves upon the previous best time bound of O(nm + n log log n). Our algorithm first determines the cycle with minimum mean length λ∗ in O(nm) time. Subsequently, it chooses node potentials so ...

Cytoplasmic dynein is a minus end-directed microtubule motor that performs distinct functions in interphase and mitosis. In interphase, dynein transports organelles along microtubules, whereas in metaphase this motor has been implicated in mitotic spindle formation and orientation as well as chromosome segregation. The manner in which dynein activity is regulated during the cell cycle, however,...

The steering of electron motion in molecules is accessible with waveform-controlled few-cycle laser light and may control the outcome of light-induced chemical reactions. An optical cycle of light, however, is much shorter than the duration of the fastest dissociation reactions, severely limiting the degree of control that can be achieved. To overcome this limitation, we extended the control me...

For arbitrary cycle-free directed graph games tree-type values are introduced axiomatically and their explicit formula representation is provided. These values may be considered as natural extensions of the tree and sink values as has been defined correspondingly for rooted and sink forest graph games. The main property for the tree value is that every player in the game receives the worth of t...

The Caccetta-Häggkvist conjecture states that if G is a finite directed graph with at least n/k edges going out of each vertex, then G contains a directed cycle of length at most k. Hamidoune used methods and results from additive number theory to prove the conjecture for Cayley graphs and for vertex-transitive graphs. This expository paper contains a survey of results on the Caccetta-Häggkvist...