A relational structure A satisfies the P(n, k) property if whenever the vertex set of A is partitioned into n nonempty parts, the substructure induced by the union of some k of the parts is isomorphic to A. The P(2, 1) property is just the pigeonhole property, (P), introduced by Cameron, and studied
Combinatorial properties of generalized hypercube graphs
β Scribed by Dyi-Rong Duh; Gen-Huey Chen; D.Frank Hsu
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 406 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0020-0190
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π SIMILAR VOLUMES
Consider a communication network G in which a limited number of link and/or node faults F might occur. A routing Ο for the network (a fixed path between each pair of nodes) must be chosen without knowing which components might become faulty. The diameter of the surviving route graph R(G, Ο)/F, where
## Abstract A hereditary property of combinatorial structures is a collection of structures (e.g., graphs, posets) which is closed under isomorphism, closed under taking induced substructures (e.g., induced subgraphs), and contains arbitrarily large structures. Given a property $\cal {P}$, we write
We consider the problem of embedding graphs into hypercubes with minimal congestion. Kim and Lai showed that for a given N-vertex graph G and a hypercube it is NP-complete to determine whether G is embeddable in the hypercube with unit congestion, but G can be embedded with unit congestion in a hype