For graphs G and H, let G H denote their Cartesian sum. This paper investigates the chromatic number and the circular chromatic number for GH. It is proved that (G H) max{ c(G)...
The problem of scheduling a parallel program given by a Directed Acyclic Graph (DAG) of tasks is a well-studied area. We present a new approach which employs Differential Evolution...
Let n be a positive integer and > 0 a real number. Let Vn be a set of n points in the unit disk selected uniformly and independently at random. Define G(, n) to be the graph w...
What is the maximum possible number, f3(n), of vectors of length n over {0, 1, 2} such that the Hamming distance between every two is even? What is the maximum possible number, g3...
We develop new structural results for apex-minor-free graphs and show their power by developing two new approximation algorithms. The first is an additive approximation for colorin...
Erik D. Demaine, MohammadTaghi Hajiaghayi, Ken-ich...