A random geometric graph Gn is constructed by taking vertices X1, . . . , Xn Rd at random (i.i.d. according to some probability distribution with a bounded density function) and...
Let S be a set of horizontal line segments, or bars, in the plane. We say that G is a bar visibility graph, and S its bar visibility representation, if there exists a one-to-one c...
Alice M. Dean, William Evans, Ellen Gethner, Joshu...
We present the first location oblivious distributed unit disk graph coloring algorithm having a provable performance ratio of three (i.e. the number of colors used by the algorit...
Mathieu Couture, Michel Barbeau, Prosenjit Bose, P...
In this paper we study the performance of a particular on-line coloring algorithm, the First-Fit or Greedy algorithm, on a class of perfect graphs namely the permutation graphs. W...
The square G2 of a graph G is the graph with the same vertex set as G and with two vertices adjacent if their distance in G is at most 2. Thomassen showed that for a planar graph ...