PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

On the computational complexity of degenerate unit distance representations of graphs
Boris Horvat, Tomaž Pisanski and Jan Kratochvil
In: 21st International Workshop on Combinatorial Algoriths, 26-28 July 2010, London, UK.

Abstract

Some graphs admit drawings in the Euclidean k-space in such a (natural) way, that edges are represented as line segments of unit length. Such embeddings are called k-dimensional unit distance representations. The embedding is strict if the distances of points representing nonadjacent pairs of vertices are different than 1. When two non-adjacent vertices are drawn in the same point, we say that the representation is degenerate. Computational complexity of nondegenerate embeddings has been studied before. We initiate the study of the computational complexity of (possibly) degenerate embeddings. In particular we prove that for every k ≥ 2, deciding if an input graph has a (possibly) degenerate k-dimensional unit distance representation is NP-hard.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:8172
Deposited By:Boris Horvat
Deposited On:21 February 2012