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maximum genus of the Generalized Permutation Graph

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Northeastern Mathematical Journal 2008年第3期24卷 189-195页

作者：马登举任韩 School of Science Nantong University Nantong Jiangsu 226007 Department of Mathematics East China Normal University Shanghai 200062

In this paper we prove that the generalized permutation graph G（n, k） is upper embeddable if it has at most two odd subcycles, and that the maximum genus of G（n, k） is more than 「β（G（n,k））/3」 in most cases.

关键词： generalized permutation graph maximum genus upper embeddable

LOWER BOUNDS ON THE maximum genus OF LOOPLESS MULTIGRAPHS

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Applied Mathematics(A Journal of Chinese Universities) 2000年第4期15卷 359-368页

作者： LiDeming LiuYanpei Dept.ofMath. CapitalNormalUniv.Beijing100037 Dept.ofMath. NorthernJiaotongUniv.Beijing100044

The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous kn... 详细信息

关键词： maximum genus lower bound multigraph.

A TIGHT LOWER BOUND ON THE maximum genus OF 3-EDGE CONNECTED LOOPLESS GRAPHS

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Acta Mathematicae Applicatae Sinica 1999年第4期15卷 361-367页

作者：李德明刘彦佩 Department of Mathematics Capital Normal University Beijing China Department of Mathematics Northern Jiaotong University Beijing China

It is shown that the lower bound on the maximum genus of a 3-edge connected loopless graph is at least one-third of its cycle rank. Moreover, this lower bound is tight. There are infinitely such graphs attaining the b... 详细信息

关键词： maximum genus 3-edge connected loopless graph lower bound

A NOTE ON THE maximum genus OF 3-EDGE-CONNECTED NONSIMPLE GRAPHS

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Applied Mathematics(A Journal of Chinese Universities) 2000年第3期15卷 247-251页

作者： Huang YuanqiuDept.of Math.,Hunan Normal Univ.,Changsha 41 0 0 81 . Email:hyqq @*** Dept. of Math. Human Normal Univ. Changsha

Let G be a 3 edge connected graph (possibly with multiple edges or loops), and let γ M(G) and β(G) be the maximum genus and the Betti number of G, respectively. Then γ M(G)≥β(G)/3 can be proved and this... 详细信息

关键词： maximum genus upper embeddable Betti defficiency.

Up-embeddability of Graphs with New Degree-sum

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Acta Mathematicae Applicatae Sinica 2017年第1期33卷 169-174页

作者： Sheng-xiang Lv Meng-da FU Yan-pei LIU School of Mathematics Hunan University of Science and Technology Department of Mathematics Bei Jing Jiaotong University

Let G be a k（k ≤ 2）-edge connected simple graph with minimal degree ≥ 3 and girth g, r = [g-1/2]. For any edge uv ∈ E（G）, if dG（u）＋ dG（v）〉2v（G） - 2（k ＋ 1）（9 - 2r）/（k ＋ 1）（2r - 1）（g - 2r）... 详细信息

Let G be a k（k ≤ 2）-edge connected simple graph with minimal degree ≥ 3 and girth g, r = [g-1/2]. For any edge uv ∈ E（G）, if dG（u）＋ dG（v）〉2v（G） - 2（k ＋ 1）（9 - 2r）/（k ＋ 1）（2r - 1）（g - 2r）＋ 2（g - 2r - 1）,then G is up-embeddable. Furthermore, similar results for 3-edge connected simple graphs are also obtained.

关键词： maximum genus up-embeddability degree-sum

A POLYNOMIAL ALGORITHM FOR FINDING THEMINIMUM FEEDBACK VERTEX SET OF A3-REGULAR SIMPLE GRAPH

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Acta Mathematica Scientia 1999年第4期19卷 375-381页

作者：李德明刘彦佩 Department of Mathematics Capital Normal University Beijing 100037 China Department of Mathematics Northern Jiaotong University Beijing 100044 China

A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vert... 详细信息

关键词： maximum genus nonseparating independent number feedback vertex set 3-regular graph adjacency matching

Up-Embeddability of Graphs with New Degree-Sum of Independent Vertices

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Journal of Mathematical Research with Applications 2012年第4期32卷 399-406页

作者： Shengxiang L1, , Yanpei LIU 2 1. Department of Mathematics, Hunan University of Science and Technology, Hunan 411201, P. R. China 2. Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. China. Department of Mathematics Hunan University of Science and Technology Hunan 411201 Department of Mathematics Beijing Jiaotong University Beijing 100044

Let G be a k(k ≤3)-edge connected simple graph with minimal degree ≥ 3,girth g,r=g12.For any independent set {a1,a2 , . . . , a 6/(4 k)} of G,if,then G is up-embeddable.

关键词： up-embeddability maximum genus independent set