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Discrete Mathematics
Volume 286, Issue 3, 28 September 2004, Pages 285-286
 
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doi:10.1016/j.disc.2004.05.012    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2004 Elsevier B.V. All rights reserved.

Note

A short proof of Fan's theoremstar, open

Feng TianE-mail The Corresponding Author

Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China

Received 12 December 2002; 
revised 17 November 2003; 
accepted 6 May 2004. 
Available online 23 August 2004.

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Abstract

In this note, we give a new short proof of the following theorem: Let G be a 2-connected graph of order n. If for any two vertices u and v with d(u,v)=2, max d(u),d(v) greater-or-equal, slantedc/2, then the circumference of G is at least c, where 3less-than-or-equals, slantcless-than-or-equals, slantn and d(u,v) is the distance between u and v in G.

Keywords: Circumference; Distance

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Discrete Mathematics
Volume 286, Issue 3, 28 September 2004, Pages 285-286
 
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