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The number of rooted Eulerian planar maps

Science China Mathematics 2008年第11期51卷 2005-2012页

作者： cai junliang LIU YanPei School of Mathematical Sciences Laboratory of Mathematics and Complex SystemsBeijing Normal UniversityBeijing 100875China Department of Mathematics Beijing Jiaotong UniversityBeijing 100044China

In this paper we provide a solution of the functional equation unsolved in the paper, by the second author, "On functional equations arising from map enumerations" that appeared in Discrete Math, 123: 93-109 (1993). It is also the number of combinatorial distinct rooted general eulerian planar maps with the valency of root-vertex, the number of non-root vertices and non-root faces of the maps as three parameters. In particular, a result in the paper, by the same author, "On the number of eulerian planar maps" that appeared in Acta Math Sinica, 12: 418-423 (1992) is simplified.

关键词： Eulerian map functional equation Lagrangian inversion 05A15 05C30

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A sufficient condition on upper embeddability of graphs

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Science China Mathematics 2010年第5期53卷 340-347页

作者： cai junliang Dong GuangHua Liu YanPei Beijing Normal Univ Sch Math Sci Lab Math & Complex Syst Beijing 100875 Peoples R China Tianjin Polytech Univ Sch Sci Dept Math Tianjin 300160 Peoples R China Beijing Jiaotong Univ Sch Sci Dept Math Beijing 100044 Peoples R China

In this paper we mainly prove that let G be a(k+1)-edge-connected simple graph of order n with girth *** G is upper embeddable if for any independent set I(G) = {vi | 1 i k2 + 2},k = 0,1,2 and the lower bound is tight.

关键词： maximum genus connected graph girth upper embeddable

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