Short Dominating Paths and Cycles in the Binary Hypercube
β Scribed by Uri Blass; Iiro Honkala; Mark G. Karpovsky; Simon Litsyn
- Publisher
- Springer
- Year
- 2001
- Tongue
- English
- Weight
- 92 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0218-0006
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π SIMILAR VOLUMES
## Abstract Let __G__ be a graph of order __n__ and define __NC(G)__ = min{|__N__(__u__) βͺ __N__(__v__)| |__uv__ β __E__(__G__)}. A cycle __C__ of __G__ is called a __dominating cycle__ or __D__β__cycle__ if __V__(__G__) β __V__(__C__) is an independent set. A __D__β__path__ is defined analogously.
A set of subgraphs C1; C2; : : : ; C k in a graph G is said to identify the vertices (resp. the edges) if the sets {j: v β Cj} (resp. {j: e β Cj}) are nonempty for all the vertices v (edges e) and no two are the same set. We consider the problem of minimizing k when the subgraphs Ci are required to
## Abstract This paper studies techniques of finding hamiltonian paths and cycles in hypercubes and dense sets of hypercubes. This problem is, in general, easily solvable but here the problem was modified by the requirement that a set of edges has to be used in such path or cycle. The main result o