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Hamiltonian cycles in 1-tough graphs

โœ Scribed by Bing Wei


Publisher
Springer Japan
Year
1996
Tongue
English
Weight
710 KB
Volume
12
Category
Article
ISSN
0911-0119

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In this article, we establish bounds for the length of a longest cycle C in a 2-connected graph G in terms of the minimum degree ฮด and the toughness t. It is shown that C is a Hamiltonian cycle or |C| โ‰ฅ (t + 1)ฮด + t.

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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).

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