Hamiltonian cycles in particular k-partite graphs
β Scribed by Jacqueline Ayel
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 242 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0095-8956
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## Abstract It is conjectured that a 2(__k__ + 1)βconnected graph of order __p__ contains __k__ + 1 pairwise disjoint Hamiltonian cycles if no two of its vertices that have degree less than 1/2 + 2__k__ are distance two apart. This is proved in detail for __k__ = 1. Similar arguments establish the
We prove that if a graph G on n > 32 vertices is hamiltonian and has two nonadjacent vertices u and u with d(u) + d(u) 3 n + z where z = 0 if n is odd and z = 1 if n is even, then G contains all cycles of length m where 3 < m < 1/5(n + 13).
We prove the following theorem. "I'neorem. If G is a balanced bipartite graph with bipartition (A, B), [A I = IBI = n, such that for any x ~ A, y ~ B, d(x) + d(y) >>-n + 2, then for any (nl, n2), ni >I 2, n -----n I + hE, G contains two independent cycles of lengths 2nl and 2n2.