Let G(V , E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product I 1 ΓI 2 Γβ’ β’ β’ΓI b , where each I i is a closed interval of unit length on the real line. The cubicity of G, denoted by cub(G), is the minimum positive in
On the Cubicity of Interval Graphs
β Scribed by L. Sunil Chandran; Mathew C. Francis; Naveen Sivadasan
- Publisher
- Springer Japan
- Year
- 2009
- Tongue
- English
- Weight
- 168 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Probe interval graphs have been introduced in the physical mapping and sequencing of DNA as a generalization of interval graphs. We prove that probe interval graphs are weakly triangulated, and hence are perfect, and characterize probe interval graphs by consecutive orders of their intrinsic cliques
## Abstract The interval number of a graph __G__ is the least natural number __t__ such that __G__ is the intersection graph of sets, each of which is the union of at most __t__ intervals, denoted by __i__(__G__). Griggs and West showed that $i(G)\le \lceil {1\over 2} (d+1)\rceil $. We describe the
## Abstract An interval graph __G__ is homogeneously representable if for every vertex __v__ of __G__ there exists an interval representation of __G__ with __v__ corresponding to an end interval. We show that the homogeneous representation of interval graphs is rooted in a deeper property of a clas