We show that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. The proof uses an efficient algorithm which a.a.s. 3colours a random 4-regular ...
This paper discusses the relation among four problems: graph testing, DNA complex screening, superimposed codes and secure key distribution. We prove a surprising equivalence relat...
Let G be the intersection graph of a finite family of convex sets obtained by translations of a fixed convex set in the plane. We show that every such graph with clique number k i...
Seog-Jin Kim, Alexandr V. Kostochka, Kittikorn Nak...
This paper addresses the basic question of how well can a tree approximate distances of a metric space or a graph. Given a graph, the problem of constructing a spanning tree in a ...
We deal with the problem of maintaining a dynamic graph so that queries of the form “is there an edge between u and v?” are processed fast. We consider graphs of bounded arbor...