Thomassen [9] conjectured that for all natural numbers k > 0 and m, every graph of minimum degree k + 1 contains a cycle of length congruent to 2m modulo k. We prove that this ...
Let P be a family of dipaths. The load of an arc is the number of dipaths containing this arc. Let π(G, P) be the maximum of the load of all the arcs and let w(G, P) be the minim...
—It has recently been shown that if we twist an arbitrary subset of edges of a mesh on an orientable surface, the resulting extended graph rotation system (EGRS) can be used to i...
Qing Xing, Ergun Akleman, Jianer Chen, Jonathan L....
We consider the question: What is the maximum flow achievable in a network if the flow must be decomposable into a collection of edgedisjoint paths? Equivalently, we wish to find a...
-An edge of a graph H with a perfect matching is a fixed edge if it either belongs to none or to all of the perfect matchings of H. It is shown that a connected plane bipartite gra...