Journal of East China Normal University(Natural Sc ›› 2006, Vol. 2006 ›› Issue (5): 72-75.

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Minimum Cycle Bases of Outplanar Graphs on the Torus(Chinese)

XU Mei1, 2, REN Han2, DANG Ying2   

  1. 1. Department of Mathematics, Huaiyin Teachers College, Huaian Jiangsu 223001, China; 2. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2005-01-04 Revised:2005-06-22 Published:2006-09-25
  • Contact: REN Han

Abstract: This paper investigated the cycle base structures of 2-connected outerplanar graphs on the torus and proved that there is a one-to-one correspondence between the minimal cycle base and two nonhomotopic noncontractible cycles with the shortest total length when $fw(G)≧ 2 and ew(G)>m,m=max{li |1≦i≦f}(l1...lf denote the length of all the non-Hamilton facial walks of G).

Key words: noncontractible cycle, minimum cycle bases, outerplanar graphs, noncontractible cycle, minimum cycle bases

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