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Minimal regular 2-graphs and applications

โœ Scribed by Hongbing Fan; Guizhen Liu; Jiping Liu


Book ID
107347362
Publisher
SP Science China Press
Year
2006
Tongue
English
Weight
569 KB
Volume
49
Category
Article
ISSN
1674-7283

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In this paper the expectation and variance of the number of 2-factors in random r-regular graphs for any fixed r 2 3 is analyzed and the asymptotic distribution of this variable is determined.

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Let G be a k-regular 2-connected graph of order n. Jackson proved that G is hamiltonian if n 5 3k. Zhu and Li showed that the upper bound 3k on n can be relaxed to q k if G is 3-connected and k 2 63. We improve both results by showing that G is hamiltonian if n 5 gk -7 and G does not belong to a res