The circulant G,(al,. . . , ak), where 0 < al < ... < a k < ( n + 1 ) / 2 , is defined as the vertex-transitive graph that has vertices ifal,. . . ,if a k (mod n) adjacent to each vertex i. In this work we show that the connected circulants of degree at least three contain all even cycles. In additi
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Pancyclicity of Hamiltonian and highly connected graphs
β Scribed by Peter Keevash; Benny Sudakov
- Book ID
- 108167482
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 229 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0095-8956
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## 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.