JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 29-34.doi: 10.6040/j.issn.1671-9352.0.2016.148

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The contractible edges of a spanning tree and a perfect matching in k-connected graphs

WANG Qian   

  1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Received:2016-04-06 Online:2016-08-20 Published:2016-08-08

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Abstract: The numbers of contractible edges of a spanning tree and a perfect matching in k-connected graphs are given. The conclusions are that if every fragment of a k-connected graph has an order more than 「k/2, then there exist at least four contractible edges on the spanning tree of this graph. Furthermore, if this graph has a perfect matching, then there exist at least 「k/2+1 contractible edges on the perfect matching.

Key words: contractible edge, perfect matching, k-connect graph, spanning tree

CLC Number: 

  • O157
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