## Abstract A double Dudeney set in __K~n~__ is a multiset of Hamilton cycles in __K~n~__ having the property that each 2βpath in __K~n~__ lies in exactly two of the cycles. A double Dudeney set in __K~n~__ has been constructed when __n__ββ₯β4 is even. In this paper, we construct a double Dudeney se
Exact coverings of 2-paths by hamilton cycles
β Scribed by Midori Kobayashi; Gisaku Nakamura
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 291 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0097-3165
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We survey some results on covering the vertices of 2-colored complete graphs by t w o paths or by t w o cycles Qf different color. W e show the role of these results i n determining path Ramsey numbers and in algorithms for finding long monochromatic paths or cycles in 2-colored complete graphs. ##
## Abstract In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph Ξ is __n__β__HCβextendable__ if it contains a path of length __n__ and if every such path is contained in some Hamilton cycle of Ξ. Similarly, Ξ is __weakly n__β__HPβ