Name
Title | ||
|---|---|---|
On the computational complexity of degenerate unit distance representations of graphs |
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 nonadjacent 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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/978-3-642-19222-7_28 | IWOCA |
Keywords | Field | DocType |
nondegenerate embeddings,euclidean k-space,k-dimensional unit distance representation,nonadjacent vertex,line segment,nonadjacent pair,computational complexity,unit length,input graph,complexity,np hard problem | Geometric graph theory,Discrete mathematics,Combinatorics,Dimension (graph theory),Vertex (geometry),Degeneracy (mathematics),Unit distance graph,Topological graph theory,Mathematics,Computational complexity theory,Unit disk graph | Conference |
Volume | ISSN | Citations |
6460 | 0302-9743 | 1 |
PageRank | References | Authors |
0.39 | 12 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Boris Horvat | 1 | 6 | 1.91 |
| Jan Kratochvíl | 2 | 1751 | 151.84 |
| Tomaž Pisanski | 3 | 214 | 44.31 |