We show how to embed a 3-connected planar graph with n vertices as a 3-polytope with small integer coordinates. The coordinates are bounded by O(27.55n ). The crucial part is the ...
Given a graph H = (V, F) with edge weights {w(e) : e F}, the weighted degree of a node v in H is {w(vu) : vu F}. We give bicriteria approximation algorithms for problems that see...
Vertex pursuit games, such as the game of Cops and Robbers, are a simplified model for network security. In these games, cops try to capture a robber loose on the vertices of the ...
The task of finding the largest subset of vertices of a graph that induces a planar subgraph is known as the Maximum Induced Planar Subgraph problem (MIPS). In this paper, some n...
Suppose we are given a sequence of n points in the Euclidean plane, and our objective is to construct, on-line, a connected graph that connects all of them, trying to minimize the...