Mutually orthogonal hamiltonian connected graphs
β Scribed by Tung-Yang Ho; Cheng-Kuan Lin; Jimmy J.M. Tan; Lih-Hsing Hsu
- Book ID
- 108052467
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 464 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0893-9659
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π SIMILAR VOLUMES
## Abstract One of the most fundamental results concerning paths in graphs is due to Ore: In a graph __G__, if deg __x__ + deg __y__ β§ |__V__(__G__)| + 1 for all pairs of nonadjacent vertices __x, y__ β __V__(__G__), then __G__ is hamiltonianβconnected. We generalize this result using set degrees.
## Abstract A __decomposition__ π’={__G__~1~, __G__~2~,β¦,__G__~__s__~} of a graph G is a partition of the edge set of G into edgeβdisjoint subgraphs __G__~1~, __G__~2~,β¦,__G__~__s__~. If __G__~__i__~β __H__ for all __i__β{1, 2, β¦, __s__}, then π’ is a decomposition of G by H. Two decompositions π’={__G
In this paper it is shown that any rn-regular graph of order 2rn (rn 3 3), not isomorphic to K, , , , or of order 2rn + 1 (rn even, rn 3 4), is Hamiltonian connected, which extends a previous result of Nash-Williams. As a corollary, it is derived that any such graph contains at least rn Hamiltonian