Given an undirected graph with edge weights, we are asked to find an orientation, i.e., an assignment of a direction to each edge, so as to minimize the weighted maximum outdegree...
In the 1960's, Tutte presented a decomposition of a 2-connected finite graph into 3-connected graphs, cycles and bonds. This decomposition has been used to reduce problems on...
We introduce and study a modi ed notion of planarity, in which two regions of a map are considered adjacent when they share any point of their boundaries not an edge, as standard...
Zhi-Zhong Chen, Michelangelo Grigni, Christos H. P...
We provide the first linear-space data structure with provable sublinear query time for exact point-topoint shortest path queries in planar graphs. We prove that for any planar gr...
Given a planar graph G, we consider drawings of G in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an i...
Mihyun Kang, Oleg Pikhurko, Alexander Ravsky, Math...