We show that if G is a connected graph with the same proper convex subgraphs as (Kn)', the Cartesian product of r copies of Kn, r >t 2, n >t 3, then [V(G)I ~> n" with equality if and only if G is isomorphic to (Kn)'. In this note we consider only connected finite undirected simple graphs. The compl
A characterization of the n-cube by convex subgraphs
โ Scribed by Patricia Vanden Cruyce
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 212 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0012-365X
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โฆ Synopsis
subgraphs as the graph of the It-dimensional cube Q,, (n 2 3), then IV(r)1 b t V(Q,,)j. Moreover, if IV'(f)\ = I VI CI,,)~, f is isomorphic to Q,,.
๐ SIMILAR VOLUMES
Let G(n, p ) denote the probability space consisting of all spanning subgraphs g of the n-cube En, and the probability is defined as ERDOS and SPENCER investigated the connectedness of such random graphs for fixed probability p , O<p<l (cf. [l]). I n this paper we study coverings of the vertex set
We consider two types of random subgraphs of the n-cube. For these models we study the asymptotic behaviour of the number of d-cubes when d = 1,2,
We consider two types of random subgraphs of the n-cube. For these models we study the asymptotic behaviour of the number of vertices of degree d.
The following combinatorial problem, which arose in game theory, is solved here: To tind a selt of vertices of ;P given size (in t.k nxube) which has a maximal number sf interconnecting edges,