journal6 ›› 2002, Vol. 23 ›› Issue (1): 21-23.

• Doctoral Forum • Previous Articles     Next Articles

Sufficiency for the Existence of Rm-EDGE CUT


  1. (1.Department of Mathematics, Zhangzhou Normal College,Zhangzhou 363000,Fujian China;2.Department of Mathematics, Xiamen University, Xiamen 361005,Fujian China)
  • Online:2002-03-15 Published:2013-01-05
  • About author:OU Jian-ping(1965-),male,was born in Guiyang County,Hunan Provinc,a doctor candidate of dept. of mathematics,Xiamen University,majors are graphs and networks.
  • Supported by:

    Supperted by Natural Science Foundation of China(19971071)

Abstract: Rm-edge cut is such an edge cut that separates a connected graph into a disconnected one with no component having order less than m. Let G be a connected graph with order at least 2m. Write c(G) for the circumference of graph G, i.e., the length of the longest cycle in G. It is proved in this paper that graph G contains Rm-edge cuts if c(G) ≥m+1. The lower bound of c(G) is sharp to some extent.

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