A kernel in a directed graph D=(V,A)is a set K of vertices of D such that no two vertices in K are adjacent and for every vertex v in V\K there is a vertex u in K,such that(v,u)is an arc of D.It is well known that the...A kernel in a directed graph D=(V,A)is a set K of vertices of D such that no two vertices in K are adjacent and for every vertex v in V\K there is a vertex u in K,such that(v,u)is an arc of D.It is well known that the problem of the existence of a kernel is NP-complete for a general digraph.Bang-Jensen and Gutin pose an interesting problem(Problem 12.3.5)in their book[Digraphs:Theory,Algorithms and Applications,London:Springer-Verlag,2000]:to characterize all circular digraphs with kernels.In this paper,we study the problem of the existence of the kernel for several special classes of circular digraphs.Moreover,a class of counterexamples is given for the Duchet kernel conjecture(for every connected kernel-less digraph which is not an odd directed cycle,there exists an arc which can be removed and the obtained digraph is still kernel-less).展开更多
The authors give an upper bound for the projective plane crossing number of a circular graph. Also, the authors prove the projective plane crossing numbers of circular graph C （8, 3） and C （9, 3） are 2 and 1, resp...The authors give an upper bound for the projective plane crossing number of a circular graph. Also, the authors prove the projective plane crossing numbers of circular graph C （8, 3） and C （9, 3） are 2 and 1, respectively.展开更多
For a general graph G, M（G） denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number xc（M（G）） equals to the chromatic number x（M（G））, ...For a general graph G, M（G） denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number xc（M（G）） equals to the chromatic number x（M（G））, which have improved some best sufficient conditions published up to date.展开更多
The vertex connectivity k(G) of a graph G is the minimum number of nodes whose deletion disconnects it. Graph connectivity is one of the most fundamental problems in graph theory. In this paper, we designed an O(n2) t...The vertex connectivity k(G) of a graph G is the minimum number of nodes whose deletion disconnects it. Graph connectivity is one of the most fundamental problems in graph theory. In this paper, we designed an O(n2) time algorithm to solve connectivity problem on circular trapezoid graphs.展开更多
The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit desi...The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.展开更多
Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 ...Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 = x^2 ＋ y^2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k ＋ 1 orders.展开更多
In this article we propose a new model for scheduling periodic tasks. The model is based on a variation of the circular chromatic number, called the multiple circular colouring of the conflict graph. We show that for ...In this article we propose a new model for scheduling periodic tasks. The model is based on a variation of the circular chromatic number, called the multiple circular colouring of the conflict graph. We show that for a large class of graphs, this new model will provide better solutions than the original circular chromatic number. At the same time, it allows us to avoid the difficulty of implementation when the fractional chromatic number is used.展开更多
本文分析了圆锯片设计及制造优化中减振降噪水平与动态稳定性的研究热点与前沿理论的演进路径,基于可视化分析软件CiteSpace,以2002—2022年中国知网和Web of Science核心合集数据库为数据来源,分别从年发文量、关键词、发文作者及发文...本文分析了圆锯片设计及制造优化中减振降噪水平与动态稳定性的研究热点与前沿理论的演进路径,基于可视化分析软件CiteSpace,以2002—2022年中国知网和Web of Science核心合集数据库为数据来源,分别从年发文量、关键词、发文作者及发文机构,对圆锯片结构设计及生产工艺的一般方法及特点进行初步探讨,根据关键词时间线及突显词对未来发展趋势进行展望。研究结果表明,2002—2022年圆锯片相关研究领域的中英文文献发文量平稳,研究机构间的合作相对分散,研究热点主要集中在圆锯片结构设计优化和生产工艺优化方面。结合关键词演变知识图谱,总结了提升圆锯片减振降噪水平及动态稳定性的方法,指明了该领域未来的研究重点和发展方向。展开更多
文摘A kernel in a directed graph D=(V,A)is a set K of vertices of D such that no two vertices in K are adjacent and for every vertex v in V\K there is a vertex u in K,such that(v,u)is an arc of D.It is well known that the problem of the existence of a kernel is NP-complete for a general digraph.Bang-Jensen and Gutin pose an interesting problem(Problem 12.3.5)in their book[Digraphs:Theory,Algorithms and Applications,London:Springer-Verlag,2000]:to characterize all circular digraphs with kernels.In this paper,we study the problem of the existence of the kernel for several special classes of circular digraphs.Moreover,a class of counterexamples is given for the Duchet kernel conjecture(for every connected kernel-less digraph which is not an odd directed cycle,there exists an arc which can be removed and the obtained digraph is still kernel-less).
基金the National Natural Science Foundation of China under Grant No.10671073Scientific Study Foundation of the Talented People Gathered by Nantong University+2 种基金Science and Technology Commission of Shanghai Municipality under Grant No.07XD14011Shanghai Leading Academic Discipline Project under Grant No.B407Natural Science Foundation of Jiangsu's Universities under Grant No.07KJB110090
文摘The authors give an upper bound for the projective plane crossing number of a circular graph. Also, the authors prove the projective plane crossing numbers of circular graph C （8, 3） and C （9, 3） are 2 and 1, respectively.
基金Supported by National Science Foundation of China (10371048)the Science Foundation of Three Gorges University.
文摘For a general graph G, M（G） denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number xc（M（G）） equals to the chromatic number x（M（G））, which have improved some best sufficient conditions published up to date.
文摘The vertex connectivity k(G) of a graph G is the minimum number of nodes whose deletion disconnects it. Graph connectivity is one of the most fundamental problems in graph theory. In this paper, we designed an O(n2) time algorithm to solve connectivity problem on circular trapezoid graphs.
文摘The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.
文摘Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 = x^2 ＋ y^2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k ＋ 1 orders.
文摘In this article we propose a new model for scheduling periodic tasks. The model is based on a variation of the circular chromatic number, called the multiple circular colouring of the conflict graph. We show that for a large class of graphs, this new model will provide better solutions than the original circular chromatic number. At the same time, it allows us to avoid the difficulty of implementation when the fractional chromatic number is used.
文摘本文分析了圆锯片设计及制造优化中减振降噪水平与动态稳定性的研究热点与前沿理论的演进路径,基于可视化分析软件CiteSpace,以2002—2022年中国知网和Web of Science核心合集数据库为数据来源,分别从年发文量、关键词、发文作者及发文机构,对圆锯片结构设计及生产工艺的一般方法及特点进行初步探讨,根据关键词时间线及突显词对未来发展趋势进行展望。研究结果表明,2002—2022年圆锯片相关研究领域的中英文文献发文量平稳,研究机构间的合作相对分散,研究热点主要集中在圆锯片结构设计优化和生产工艺优化方面。结合关键词演变知识图谱,总结了提升圆锯片减振降噪水平及动态稳定性的方法,指明了该领域未来的研究重点和发展方向。
