Journal of East China Normal University(Natural Sc ›› 2008, Vol. 2008 ›› Issue (3): 37-44,1.

• Article • Previous Articles     Next Articles

Unicyclic subgraphs in 2-connected graphs(Chinese)

LI Shi-yin, BAI Yun, DONG Qian, REN Han   

  1. Department of Mathematics, East China Normal University, Shanghai 20062, China
  • Received:2007-05-23 Revised:2007-10-23 Online:2008-05-25 Published:2008-05-25
  • Contact: REN Han

Abstract: This paper proved the following results:(1) The ⊙-graph of a 2-connected graph is 2(p-1) connected; (2) if a 2-connected graph G has two unicyclic spanning subgraphs and the number of one-valent vertices of these two subgraphs are respectively m and n (m<n), then for any integer k:m≦k≦n,there exist at least 2(p-1) unicyclic subgraphs of graph G whick have k one-valent vertices. Here, p is the dimension of the cycle space of G.

Key words: 2-connected graph, unicyclic spanning subgraph, ⊙-graph, adjacent ⊙-graph, cut edge, 2-connected graph, unicyclic spanning subgraph, ⊙-graph, adjacent ⊙-graph

CLC Number: