A barycentric mapping of a planar graph is a plane embedding in which every internal vertex is the average of its neighbours. A celebrated result of Tutte’s [16] is that if a pl...
A visibility representation of a graph G is to represent the nodes of G with non-overlapping horizontal line segments such that the line segments representing any two distinct adja...
Position-based routing protocols in ad hoc networks combine a forwarding strategy with a recovery algorithm. The former fails when there are void regions or physical obstacles tha...
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...
The first-fit chromatic number of a graph is the number of colors needed in the worst case of a greedy coloring. It is also called the Grundy number, which is defined to be the max...