In this paper we present a method for analyzing a general class of random ## Ε½ . walks on the n-cube and certain subgraphs of it . These walks all have the property that the transition probabilities depend only on the level of the point at which the walk is. For these walks, we derive sharp bound
On Random Sections of the Cube
β Scribed by Y. Lonke
- Publisher
- Springer
- Year
- 2000
- Tongue
- English
- Weight
- 86 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0179-5376
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π SIMILAR VOLUMES
The N-cube is a graph with 2 N vertices and N 2 Ny1 edges. Suppose indepen- dent uniform random edge weights are assigned and let T be the spanning tree of minimal Ε½ . y 1 N Ο± y3 total weight. Then the weight of T is asymptotic to N 2 Γ i as N Βͺ Ο±. Asymp-is1 totics are also given for the local stru
vertices are adjacent if they differ in exactly one coordinate. Random induced subgraphs, . with probability . The first theorem shows that for s c ln n rn there exists n n a unique largest component in β« -Q Q n which contains almost all vertices and that n β£ Ε½ . the size of the second largest comp