We prove that any k-regular directed graph with no parallel edges contains a collection of at least Ω(k) edge-disjoint cycles, conjecture that in fact any such graph contains a collection of at least ( k+1 2 ) disjoint cycles, and note that this holds for k ≤ 3. In this paper we consider the maximum size of a collection of edge-disjoint cycles in a directed graph. We pose the following conjectu...

We derive a formula for the generating function of d-irreducible bipartite planar maps with several boundaries, i.e. having several marked faces of controlled degrees. It extends a formula due to Collet and Fusy for the case of arbitrary (non necessarily irreducible) bipartite planar maps, which is recovered by taking d = 0. As an application, we obtain an expression for the number of d-irreduc...

In this paper, a theorem is proved that generalizes several existing amalgamation results in various ways. The main aim is to disentangle a given edge-colored amalgamated graph so that the result is a graph in which the edges are shared out among the vertices in ways that are fair with respect to several notions of balance (such as between pairs of vertices, degrees of vertices in the both grap...