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The genus polynomials of cross-ladder digraphs in orientable surfaces

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Science China Mathematics 2008年第5期51卷 889-896页

作者： HAO RongXia liu yanpei Department of Mathematics Beijing Jiaotong UniversityBeijing 100044China

Some results about the genus distributions of graphs are known,but little is known about those of *** this paper,the method of joint trees initiated by liu is generalized to compute the embedding genus distributions of digraphs in orientable *** genus polynomials for a new kind of 4-regular digraphs called the cross-ladders in orientable surfaces are *** results are close to solving the third problem given by Bonnington et al.

关键词： graph genus distribution genus surfaces 05C10

The number of rooted Eulerian planar maps

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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

Up-embeddability via girth and the degree-sum of adjacent vertices

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Science China Mathematics 2009年第3期52卷 597-604页

作者： DONG GuangHua liu yanpei Department of Mathematics Beijing Jiaotong UniversityBeijing 100044China Department of Mathematics School of ScienceTianjin Polytechnic UniversityTianjin 300160China

Let G be a simple graph of order n and girth g. For any two adjacent vertices u and v of G, if d G (u) + d G (v) ? n ? 2g + 5 then G is up-embeddable. In the case of 2-edge-connected (resp. 3-edge-connected) graph, G is up-embeddable if d G (u) + d G (v) ? n ? 2g + 3 (resp. d G (u) + d G (v) ? n ? 2g ?5) for any two adjacent vertices u and v of G. Furthermore, the above three lower bounds are all shown to be tight.

关键词： maximum genus up-embeddable order girth 05C10

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

STRONG EMBEDDING OF HP-GRAPHS ON SURFACE WITH HIGHER GENUS

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Journal of Systems Science & Complexity 2006年第3期19卷 441-446页

作者： Erling WEI yanpei liu Department of Mathematics Renmin University of China Beijing 100872 China. Department of Mathematics Northern Jiaotong University Beijing 100044 China.

In 1990, Bondy posed the small circuit double cover （SCDC） conjecture： Every 2-connected graph has a circuit double cover （CDC） with the number of circuits less than ｜v｜（the order of the vertex set V）. The strong embedding conjecture states that every 2-connected graph has a strong embedding on some surface in which the boundary of each face is a circuit. In this paper, HP-graph is defined as the graph which has a strong embedding on the projective plane with one face of valence ｜V｜ and the other faces of valence 3. And it is proved that the HP-graph has a strong embedding with ｜V｜ - 1 or less faces on some surface, which confirms both the SCDC conjecture and the strong embedding conjecture.

关键词： CDC embedding genus HP-graph surface.

ENUMERATION OF ROOTED PLANAR HALIN MAPS

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Applied Mathematics(A Journal of Chinese Universities) 1999年第1期14卷 117-121页

作者： Ren Han\ liu yanpei Dept. of Math. Northern Jiaotong Univ. Beijing

Abstract A Halin map is a kind of planar maps oriented by a tree. In this paper the rooted halin maps with the vertex partition as parameters are enumerated such that a famous result on rooted trees due to Harary, Prins, and Tutte is deduced as a special case. Further, by using Lagrangian inversion to obtain a number of summation free formulae directly, the various kinds of rooted Halin maps with up to three parameters have been counted.

关键词： 1991 MR Subject Classification 05C45

Genus distribution of ladder type and cross type graphs

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Science China Mathematics 2009年第8期52卷 1760-1768页

作者： WAN LiangXia FENG KeQin liu yanpei WANG DianJun Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China Department of Mathematics Beijing Jiaotong UniversityBeijing 100044China

In this paper a method is given to calculate the explicit expressions of embedding genus distribution for ladder type graphs and cross type graphs. As an example, we refind the genus distri- bution of the graph Jn whi... 详细信息

关键词： embedding genus distribution joint tree surface genus 05C10 05C30

A CHARACTERIZATION OF EMBEDDABILITY OF GRAPHS ON SURFACES

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Applied Mathematics:A Journal of Chinese Universities 1998年第2期 39-44页

作者： liu YING AND liu yanpei

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THE MAXIMUM GENUS OF A 3-REGULAR SIMPLICIAL GRAPH

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Applied Mathematics:A Journal of Chinese Universities 1999年第2期 81-92页

作者： Li Deming\ liu yanpei

§１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｍａｘｉｍｕｍｇｅｎｕｓｏｆａｃｏｎｎｅｃｔｅｄｇｒａｐｈＧ＝（Ｖ，Ｅ），ｄｅｎｏｔｅｄｂｙγＭ（Ｇ），ｉｓｔｈｅｍａｘ－ｉｍｕｍｉｎｔｅｇｅｒｋａｍｏｎｇｔｈｅｇｅｎｅｒａｓｕｃｈ...

§１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｍａｘｉｍｕｍｇｅｎｕｓｏｆａｃｏｎｎｅｃｔｅｄｇｒａｐｈＧ＝（Ｖ，Ｅ），ｄｅｎｏｔｅｄｂｙγＭ（Ｇ），ｉｓｔｈｅｍａｘ－ｉｍｕｍｉｎｔｅｇｅｒｋａｍｏｎｇｔｈｅｇｅｎｅｒａｓｕｃｈｔｈａｔｔｈｅｒｅｉｓａｎｅｍｂｅ...

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