In early 2000’s, Rivest [1,2] and Micali [2] introduced the notion of transitive signature, which allows a third party with public key to generate a valid signature for a composed edge (vi,vk), from the signatures for two edges (vi,v j) and (v j,vk). Since then, a number of works, including [2,3,4,5,6], have been devoted on transitive signatures. Most of them address the undirected transitive s...

Undirected graphs of pathwidth at most one are characterized by two forbidden minors i.e., (i) K3 the complete graph on three vertices and (ii) S2,2,2 the spider graph with three legs of length two each [BFKL87]. Directed pathwidth is a natural generalization of pathwidth to digraphs. In this paper, we prove that digraphs of directed pathwidth at most one are characterized by a finite number of...

We study the relation between the directed polymer and the directed percolation models, for the case of a disordered energy landscape where the energies are taken from bimodal distribution. We find that at the critical concentration of the directed percolation, the directed polymer undergoes a transition from the directed polymer universality class to the directed percolation universality class...