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16 papers · 1 filter
Noncrossing Longest Paths and Cycles
Greg Aloupis, Ahmad Biniaz, Prosenjit Bose +7
Edge crossings in geometric graphs are sometimes undesirable as they could lead to unwanted situations such as collisions in motion planning and inconsistency in VLSI layout. Short…
Observation Routes and External Watchman Routes
Adrian Dumitrescu, Csaba D. Tóth
We introduce the Observation Route Problem () defined as follows: Given a set of pairwise disjoint compact regions in the plane, find a shortest tour (route) such…
Minimum Weight Euclidean -Spanners
Csaba D. Tóth
Given a set of points in the plane and a parameter , a Euclidean -spanner is a geometric graph that contains, for all ,…
Hop-Spanners for Geometric Intersection Graphs
Jonathan B. Conroy, Csaba D. Tóth
A -spanner of a graph is a subgraph that contains a -path of length at most for every . It is known that every -vertex graph admits a $(…
Axis-Aligned Square Contact Representations
Andrew Nathenson
We introduce a new class of bipartite plane graphs and prove that each graph in admits a proper square contact representation. A contact between two squ…
Rainbow polygons for colored point sets in the plane
David Flores-Peñaloza, Mikio Kano, Leonardo Martínez-Sandoval +5
Given a colored point set in the plane, a perfect rainbow polygon is a simple polygon that contains exactly one point of each color, either in its interior or on its boundary. Let…