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极大平面图在不可定向曲面上强嵌入的一个注记
引用本文:刘同,刘彦佩.极大平面图在不可定向曲面上强嵌入的一个注记[J].高校应用数学学报(英文版),2001,16(2).
作者姓名:刘同  刘彦佩
作者单位:Liu Tongyin Liu Yanpei Dept.ofMath.,NorthernJiaotongUniv.,Beijing100044.
基金项目:Supported by NNSFC(699730 0 1 )
摘    要:§ 1 IntroductionA strong embeddingμ( G) of a graph G in a surface S is such an embedding thateachface boundary of the surface is a circuit.( A strong embedding is also sometimes called acircular embedding,see1 ] orclosed2 -cell embedding2 ] ) .Graphsconsidered here are sim-ple( that is,they have no loops or multiple edges) .Terminology here follows those in3] .In1 ] ,Richter,Seymour and Siran proved that every3-connected planar graph canbe strongly embedded on some non-orientable sur…


A NOTE ON STRONG EMBEDDINGS OF MAXIMAL PLANAR GRAPHS ON NON-ORIENTABLE SURFACES
Liu Tongyin,Liu Yanpei.A NOTE ON STRONG EMBEDDINGS OF MAXIMAL PLANAR GRAPHS ON NON-ORIENTABLE SURFACES[J].Applied Mathematics A Journal of Chinese Universities,2001,16(2).
Authors:Liu Tongyin  Liu Yanpei
Abstract:In this paper, it is shown that for every maximal planar graph G=(V,E) , a strong embedding on some non orientable surface with genus at most |V(G)|-22 is admitted such that the surface dual of G is also a planar graph. As a corollary, an interpolation theorem for strong embeddings of G on non orientable surfaces is obtained.
Keywords:Surface  strong embedding  maximal planar graph  
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