检索结果-南通市图书馆

A 3-color Theorem on Plane Graphs without 5-circuits

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2007年第6期23卷 1059-1062页

作者： bao gang xu School of Math. & Computer Science Nanjing Normal University Nanjing 210097 P. R. China

In this paper, we prove that every plane graph without 5-circuits and without triangles of distance less than 3 is 3-colorable. This improves the main result of Borodin and Raspaud [Borodin, O. V., Raspaud, A.： A sufficient condition for planar graphs to be 3-colorable. Journal of Combinatorial Theory, Ser. B, 88, 17-27 （2003）], and provides a new upper bound to their conjecture.

关键词： plane graph circuit coloring

Connectivity of Minimum Non-5-injectively Colorable Planar Cubic Graphs

在线全文

学校读者我要写书评

暂无评论

Journal of the Operations Research Society of China 2020年第1期8卷 105-116页

作者： Jing Jin bao-gang xu Institute of Mathematics School of Mathematical SciencesNanjing Normal UniversityNanjing 210023China College of Taizhou Nanjing Normal UniversityTaizhou 225300JiangsuChina

Suppose that G is a planar cubic graph withχi(G)>*** show that ifχi(H)<χi(G)for each planar cubic graph H of order less thanG,thenG is either a 3-connected simple planar cubic graph,or a planar graph obtained from a simple cubic 3-connected planar graph by adding some *** shows that a minimum non-5-injectively colorable simple planar cubic graph must be 3-connected.

关键词： Planar cubic graphs Connectivity 3-connected Injective coloring

A Note on Strong Edge Coloring of Sparse Graphs

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2019年第4期35卷 577-582页

作者： Wei DONG Rui LI bao gang xu School of Information and Engineering Nanjing Xiaozhuang University Department of Mathematics College of Science Hohai University School of Mathematical Sciences Nanjing Normal University

A strong edge coloring of a graph is a proper edge coloring where the edges at distance at most 2 receive distinct colors. The strong chromatic index χ'_s(G) of a graph G is the minimum number of colors used in a strong edge coloring of G. In an ordering Q of the vertices of G, the back degree of a vertex x of G in Q is the number of vertices adjacent to x, each of which has smaller index than x in Q. Let G be a graph of maximum degree Δ and maximum average degree at most 2 k. Yang and Zhu [J. Graph Theory, 83, 334–339(2016)] presented an algorithm that produces an ordering of the edges of G in which each edge has back degree at most 4 kΔ-2 k in the square of the line graph of G, implying that χ'_s(G) ≤ 4 kΔ-2 k + 1. In this note, we improve the algorithm of Yang and Zhu by introducing a new procedure dealing with local structures. Our algorithm generates an ordering of the edges of G in which each edge has back degree at most(4 k-1)Δ-2 k in the square of the line graph of G, implying that χ'_s(G) ≤(4 k-1)Δ-2 k + 1.

关键词： Strong edge coloring maximum average degree sparse graph

2-divisibility of Some Odd Hole Free Graphs

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2022年第3期38卷 710-718页

作者： Wei DONG Jia-lei SONG bao-gang xu School of Information and Engineering Nanjing Xiaozhuang UniversityNanjing 211171China Institute of Mathematics School of Mathematical SciencesNanjing Normal UniversityNanjing 210023China

Let G be a *** say that G is 2-divisible if for each induced subgraph H of G,either V(H)is a stable set,or V(H)can be partitioned into two sets A and B such thatω(H[A])<ω(H)andω(H[B])<ω(H).A hole is an induced cycle of length at least 4,a bull is a graph consisting of a triangle with two disjoint pendant edges,a diamond is the graph obtained from K4 by removing an edge,a dart denotes the graph obtained from a diamond by adding a pendant edge to one vertex of degree 3,and a racket denotes the graph obtained from a diamond by adding a pendant edge to one vertex of degree *** this paper,we prove that every{odd hole,H}-free graph is 2-divisible,where H is a dart,or a racket,or a *** corollaries,X(G)≤min{2ω^(G)-1,(ω^(G)/2+1)}if G is{odd hole,dart}-free,or{odd hole,racket}-free,or{odd hole,bull}-free.

关键词： hole odd hole 2-divisibility

Design of Discrete-time Repetitive Control System Based on Two-dimensional Model

在线全文

学校读者我要写书评

暂无评论

International Journal of Automation and computing 2012年第2期9卷 165-170页

作者： Song-Gui Yuan Min Wu bao-gang xu Rui-Juan Liu School of Information Science and Engineering Central South University Changsha 410083 PRC School of Electrical and Information Engineering Changsha University of Science and Technology Changsha 410076 PRC

This paper presents a novel design method for discrete-time repetitive control systems （RCS） based on two-dimensional （2D） discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and linear matrix inequality （LMI） method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI of the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.

关键词： Linear systems learning control discrete-time repetitive control two-dimensional (2D) systems linear matrix inequality.

A Structural Theorem on Embedded Graphs and Its Application to Colorings

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2009年第1期25卷 47-50页

作者： bao gang xu Xiao xu LUNanjing Normal University, 122 Ninghai Road, Nanjing, 210097, P. R. China Nanjing Normal University 122 Ninghai Road Nanjing 210097 P. R. China

In this paper, a Lebesgue type theorem on the structure of graphs embedded in the surface of characteristic σ≤ 0 is given, that generalizes a result of Borodin on plane graphs. As a consequence, it is proved that every such graph without i-circuits for 4 ≤ i ≤ 11 - 3σ is 3-choosable, that offers a new upper bound to a question of Y. Zhao.

关键词： circuit embedded graph coloring

Some Results on Graph Products Determined by Their Spectra

在线全文

学校读者我要写书评

暂无评论

Journal of Mathematical Research and Exposition 2010年第2期30卷 227-232页

作者： Ke Xiang xu Juan YAN bao gang xu Zhi Ren SUN College of Science Nanjing University of Aeronautics & Astronautics Jiangsu 210016 P. R. China College of Mathematics and System Sciences Xinjiang University Xinjiang 830046 P. R. China School of Mathematics Nanjing Normal University Jiangsu 210046 P. R. China

In this paper, we prove that some Kronecker products of G and K2 are determined by their spectra where the graph G is also determined by its spectrum. And a problem for further researches is proposed.

关键词： Kronecker product spectrum of graph determined by spectra.

在线全文

学校读者我要写书评

暂无评论

一类无奇洞图的色数

数学学报（中文版） 2024年第5期67卷 830-842页

作者：宋佳磊许宝刚南京师范大学数学科学学院数学研究所南京210023

给定图G,我们称G中长度至少为4的导出圈为G的洞,长度为奇数或偶数的洞分别被称为是奇洞或偶洞.我们用HVN来表示一个由K_(4)添加一个点并向K_(4)连两条边所得的图,用H表示长为7的圈的补图.Chudnovsky等人在[*** B,2010,100:313-331]中证... 详细信息

给定图G,我们称G中长度至少为4的导出圈为G的洞,长度为奇数或偶数的洞分别被称为是奇洞或偶洞.我们用HVN来表示一个由K_(4)添加一个点并向K_(4)连两条边所得的图,用H表示长为7的圈的补图.Chudnovsky等人在[*** B,2010,100:313-331]中证明了每一个无奇洞且无K_(4)的图是4-可染的,且其色数为4当且仅当其含有H为导出子图.在本文中,我们将这一结论推广到无奇洞且无HVN的图类上.设G是一个无奇洞且无HVN的图,我们证明了若G含有H为导出子图,则G有一个特殊的割集或者属于两类特殊图,作为推论我们证明了X(G)≤ω(G)+1,且等号成立当且仅当ω(G)=3且G含有H为导出子图,从而完全确定了这类图的色数.

关键词：奇洞色数团数

在线全文

学校读者我要写书评

暂无评论

图的k部划分的一个注记

数学学报（中文版） 2016年第2期59卷 247-252页

作者：刘木伙许宝刚华南农业大学应用数学系广州510642 南京师范大学数学科学学院数学研究所南京210023

设k≥2是一个整数。本文证明了任意有m条边的图都存在一个顶点的划分V_1,V_2…,V_k,使得e(V_1,V_2…,V_k)≥k-1/k m+k-1/2k((2m+1/4)~1/2-1/2)-(k-2)~2/8k,且max{e(V_i):1≤i≤k}≤m/k^2+(k-1)/2k^2((2m+1/4)~1/2-1/2+3/8-7k-4/8k^2.我们的结果改进了[Fan G.,Hou J.,Zeng Q.,A bound for judicious k-partitions of graphs,Discrete ***.,2014,179:86—99]的主要结论.

关键词：图的划分界图