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 รI 2 รโข โข โขรI 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 sphericity and cubicity of graphs
โ Scribed by Peter C Fishburn
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 535 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The sphericity of a graph G is the smallest integer n such that G can be represented as the intersection graph of a family of unit-diameter spheres in Euclidean n-space E n. We determine here the sphericities of the graph of semiregular polyhedra in E 3 except a few prisms.
It is proved that given any number of graphs of order at most n, the sphericity of their join does not exceed 2(n-1). We introduce an adjacency relation into Euclidean n-space E" so that it may be regarded as an infinite graph: Two points x and y of E" are defined to be adjacent if and only if 0<[x
Bermond et al. [2] conjectured that the edge set of a cubic graph G can be partitioned into two k-linear forests, that is to say two forests whose connected components are paths of length at most k, for all k >/5. We shall prove a weaker result that the statement is valid for all k/> 18. All graphs
In this paper we present a short algebraic proof for a generalization of a formula of R. Penrose, Some applications of negative dimensional tensors, in: Combinatorial Mathematics and its Applications Welsh (ed.), Academic Press, 1971, pp. 221-244 on the number of 3-edge colorings of a plane cubic gr