The regularity lemma of Szemer´edi gives a concise approximate description of a graph via a so called regular-partition of its vertex set. In this paper we address the following ...
. Dirac. Some theorems on abstract graphs. Proc. London Math. Soc. (3), 2:69–81, 1952. [2] Hikoe Enomoto and Katsuhiro Ota. Partitions of a graph into paths with prescribed endve...
Let G be a directed edge-weighted graph and let P be a shortest path from s to t in G. The replacement paths problem asks to compute, for every edge e on P, the shortest s-to-t pat...
Abstract. We present algorithmic lower bounds on the size of the largest independent sets of vertices in a random d-regular graph. Our bounds hold with probability approaching one ...
Abstract— Thorup and Zwick, in their seminal work, introduced the approximate distance oracle, which is a data structure that answers distance queries in a graph. For any integer...