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Remarks on the Lower Bounds for the Average Genus

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Acta Mathematicae Applicatae Sinica 2011年第3期27卷 517-526页

作者： Yi-chao Chen College of mathematics and econometrics Hunan University 410082 Changsha China

Let G be a graph of maximum degree at most four. By using the overlap matrix method which is introduced by B. Mohar, we show that the average genus of G is not less than 1/3 of its maximum genus, and the bound is best... 详细信息

关键词： average genus lower bound girth overlap matrix

On Total Colorings of Some Special 1-planar Graphs

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Acta Mathematicae Applicatae Sinica 2017年第3期33卷 607-618页

作者： Lin SUN Jian-liang WU Hua CAI Department of Mathematics Changji University School of Mathematics Shandong University

A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we verify the total coloring conjecture for every 1-planar graph G if either △（G） ≥9 and g（G）≥ 4, or △（G） ≥ 7 and g（G）≥5, where △（G） is the maximum degree of G and g（G） is the girth of G.

关键词： 1-planar graph total coloring discharging method girth r-minimal graph

New Upper Bounds on Linear Coloring of Planar Graphs

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Acta Mathematica Sinica,English Series 2012年第6期28卷 1187-1196页

作者： Bin LIU Gui Zhen LIU Department of Mathematics Ocean University of China School of Mathematics Shandong University

A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc（G） of the graph G is the smallest number of colors in a linear coloring of G. In this paper, it is proved that every planar graph G with girth g and maximum degree A has （1） lc（G） ≤ △ ＋ 21 if △ ≥ 9; （2） lc（G） ≤[△/2]＋ 7 if g≥5; （3） lc（G） ≤ [△/2]＋2ifg≥7and△ ≥7.

关键词： Linear coloring planar graph girth

Low complexity construction for quasi-cyclic low-density parity-check codes by Progressive-Block Growth

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Science China(Information Sciences) 2011年第2期54卷 371-380页

作者： REN PinYi1, YUAN Qiang2, WANG Rui1 & CAI Jun3 1School of Electronic Engineering, Xi’an Jiaotong University, Xi’an 710049, China 2Wuhan Ordnance Noncommissioned Officers Academy, Wuhan 430075, China 3Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6, Canada School of Electronic Engineering Xi’an Jiaotong University Xi’an China Wuhan Ordnance Noncommissioned Officers Academy Wuhan China Department of Electrical & Computer Engineering University of Manitoba Winnipeg Canada

In this paper, a novel method for constructing quasi-cyclic LDPC codes with low complexity is proposed. By choosing each circulant permutation matrix sequentially, the proposed method ensures that the current circulant permutation matrix forms no cycles of length smaller than g with the existent circulant permutation matrices. The construction complexity of the proposed algorithm is much lower than that of the random construction. Simulation results show that the proposed QC-LDPC codes can outperform both the random regular LDPC codes with short to moderate block lengths, and the proposed construction method LDPC codes based on the finite geometries in terms of bit-error-rate (BER).

关键词： quasi-cyclic (QC) LDPC (low-density parity-check) codes circulant permutation matrix girth

On a New Extension of the Zero-Divisor Graph

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Algebra Colloquium 2020年第3期27卷 469-476页

作者： A.Cherrabi H.Essannouni E.Jabbouri A.Ouadfel Laboratory of Mathematics Computing and Applications-Information Security(LabMia-SI)Faculty of SciencesMohammed V University in RabatRabatMorocco

In this paper,we introduce a new graph whose vertices are the non-zero zerodivisors of a commutativc ring R、and for distincts elements x and y in the set Z(R)^(*)of the non-zero zero-divisors of R,x and y are adjacent if and only if xy=0 or x+y∈Z(R).We present some properties and examples of this graph,and we study its relationship with the zero-divisor graph and with a subgraph of the total graph of a commutative ring.

关键词： finite commutative ring graph diameter girth

Group Edge Choosability of Planar Graphs without Adjacent Short Cycles

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Acta Mathematica Sinica,English Series 2013年第11期29卷 2079-2086页

作者： Xin ZHANG Gui Zhen LIU Department of Mathematics Xidian University School of Mathematics Shandong University

In this paper, we prove that 2-degenerate graphs and some planar graphs without adjacent short cycles are group （△ （G）＋1）-edge-choosable, and some planar graphs with large girth and maximum degree are group △（... 详细信息

关键词： Group edge coloring list coloring planar graphs short cycles girth

Linear coloring of graphs embeddable in a surface of nonnegative characteristic

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Science China Mathematics 2009年第5期52卷 991-1003页

作者： WANG WeiFan LI Chao Department of Mathematics Zhejiang Normal UniversityJinhua 321004China

A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest number of colors in a linear coloring of G. In this paper, we prove that every graph G with girth g(G) and maximum degree Δ(G) that can be embedded in a surface of nonnegative characteristic has lc(G) = Δ(2G )+ 1 if there is a pair (Δ, g) ∈ {(13, 7), (9, 8), (7, 9), (5, 10), (3, 13)} such that G satisfies Δ(G) Δ and g(G) g.

关键词： linear coloring graph of nonnegative characteristic girth maximum degree

Improved Upper Bound for Generalized Acyclic Chromatic Number of Graphs

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Acta Mathematicae Applicatae Sinica 2018年第4期34卷 798-800页

作者： Jian-sheng CAI Xu-ding ZHU School of Mathematics and Information Sciences Weifang University Weifang 261061 China Department of Mathematics Zhejiang Normal University Jinhua 321004 China

A vertex coloring of a graph G is called r-acyclic if it is a proper vertex coloring such that every cycle D receives at least min{｜D｜, r} colors. The r-acyclic chromatic number of G is the least number of colors in an r-acyclic coloring of G. We prove that for any number r ≥ 4, the r-acyclic chromatic number of any graph G with maximum degree △ ≥ 7 and with girth at least（r-1）△ is at most（4r-3）△.

关键词： girth coloring acyclic coloring τ-acyclic coloring Lopsided local lemma

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.Then 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 ti... 详细信息

关键词： maximum genus connected graph girth upper embeddable