This paper considers the Euler tour of an uncertain random graph, in which some edges exist with some degrees in uncertain measure and others exist with some degrees in probability measure. The concept of Euler index of an uncertain random graph is proposed first, and then a method to calculate the Euler index of an uncertain random graph is given. In addition, some properties of the Euler inde...

For a given graph G of minimum degree at least k, let Gp denote the random spanning subgraph of G obtained by retaining each edge independently with probability p = p(k). We prove that if p (log k + log log k + ωk(1))/k, where ωk(1) is any function tending to infinity with k, then Gp asymptotically almost surely contains a cycle of length at least k + 1. When we take G to be the complete graph ...

We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability pF for the existence of Maker’s strategy to claim a member of F in the unbiased game played on the edges of random graph G(n, p), for various target families F of winning sets. More generally, for each probability above this threshold we study the smallest bias...

Robotic systems may frequently come across similar manipulation planning problems that result in motion plans. Instead of each problem from scratch, it is preferable to leverage previously computed plans, i.e., experiences, ease the planning. Different approaches have been proposed exploit prior information on novel task instances. These methods, however, rely a vast repertoire experiences and ...