Journal of East China Normal University(Natural Sc ›› 2006, Vol. 2006 ›› Issue (5): 66-71.

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Maximum Genus and 1-Factors of Near-Triangulation Graphs

LU Chang-qing1,2, REN Han1   

  1. 1. Department of Mathematics, East China Normal University, Shanghai } 200062, China 2. Department of Mathematics, Zaozhuang University, Zaozhuang Shandong 277160, China
  • Received:2005-01-07 Revised:2005-03-18 Online:2006-09-25 Published:2012-11-27

Abstract: This paper proved that if the geometric dual G*of a near-triangulation plane graph G contains a set of [1/2φ] independent edges, then the maximum genus γM(G) of G is at least [1/2β(G)]-1 where φ and β(G)$represent the number of faces of plane G and the Betti number of G. In particular, γM(G) = 1/2β(G) if
φ=0 mod2. As applications, several known results are presented.

Key words: maximum genus, upper-embedding, Betti number, 1-factor, near-triangulation  ,

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