This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be i...This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.展开更多
Let γ f(G) and γ~t f(G) be the fractional domination number and fractional total domination number of a graph G respectively. Hare and Stewart gave some exact fractional domination number of P n...Let γ f(G) and γ~t f(G) be the fractional domination number and fractional total domination number of a graph G respectively. Hare and Stewart gave some exact fractional domination number of P n×P m (grid graph) with small n and m . But for large n and m , it is difficult to decide the exact fractional domination number. Motivated by this, nearly sharp upper and lower bounds are given to the fractional domination number of grid graphs. Furthermore, upper and lower bounds on the fractional total domination number of strong direct product of graphs are given.展开更多
The main contribution in this article is threefold:(1)we show the necessary and sufficient condition for graphs to be fractional(g,f)-covered which can be expressed in different forms,and extended to fractional(g,f,m)...The main contribution in this article is threefold:(1)we show the necessary and sufficient condition for graphs to be fractional(g,f)-covered which can be expressed in different forms,and extended to fractional(g,f,m)-covered graphs;(2)the concept of fractional-critical covered graph is put forward and its necessary and sufficient condition is given;(3)we present the degree condition for a graph to be fractional(g,f,n′,m)-critical covered,and show that degree bound is sharp when m is small.Moreover,the related result in fractional(a,b,n′,m)-critical covered setting is also verified.展开更多
The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicat...The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.展开更多
We consider the block matrices and 3-dimensional graph manifolds associated with a special type of tree graphs. We demonstrate that the linking matrices of these graph manifolds coincide with the reduced matrices obta...We consider the block matrices and 3-dimensional graph manifolds associated with a special type of tree graphs. We demonstrate that the linking matrices of these graph manifolds coincide with the reduced matrices obtained from the Laplacian block matrices by means of Gauss partial diagonalization procedure described explicitly by W. Neumann. The linking matrix is an important topological invariant of a graph manifold which is possible to interpret as a matrix of coupling constants of gauge interaction in Kaluza-Klein approach, where 3-dimensional graph manifold plays the role of internal space in topological 7-dimensional BF theory. The Gauss-Neumann method gives us a simple algorithm to calculate the linking matrices of graph manifolds and thus the coupling constants matrices.展开更多
We present a new algorithm for the fast expansion of rational numbers into continued fractions. This algorithm permits to compute the complete set of integer Euler numbers of the sophisticate tree graph manifolds, whi...We present a new algorithm for the fast expansion of rational numbers into continued fractions. This algorithm permits to compute the complete set of integer Euler numbers of the sophisticate tree graph manifolds, which we used to simulate the coupling constant hierarchy for the universe with five fundamental interactions. Moreover, we can explicitly compute the integer Laplacian block matrix associated with any tree plumbing graph. This matrix coincides up to sign with the integer linking matrix (the main topological invariant) of the graph manifold corresponding to the plumbing graph. The need for a special algorithm appeared during computations of these topological invariants of complicated graph manifolds since there emerged a set of special rational numbers (fractions) with huge numerators and denominators;for these rational numbers, the ordinary methods of expansion in continued fraction became unusable.展开更多
根据超声心动图准确分析左心室轮廓和射血分数对于心血管疾病诊断意义重大.但现有方法存在左心室分割和射血分数预测之间缺乏关联性、左心室分割关键点易于出现离群点和突变点、方法存储和计算开销大、解释性不佳等问题,为此提出一种基...根据超声心动图准确分析左心室轮廓和射血分数对于心血管疾病诊断意义重大.但现有方法存在左心室分割和射血分数预测之间缺乏关联性、左心室分割关键点易于出现离群点和突变点、方法存储和计算开销大、解释性不佳等问题,为此提出一种基于先验知识引导的轻量级图卷积方法EchoGPK(Echo Guided by Priori Knowledge),以心脏的结构和运动特性、相邻心肌的相似性等先验知识为引导,设计了计算高效的螺旋聚合函数和深度压缩的多头偏心聚合解码器,实现了图卷积结构的轻量化.方法基于临床医生的普遍经验提出了适度利用左心室轮廓的多任务射血分数预测网络,建立了左心室分割和射血分数预测之间的关联性,增强了推理的可解释性;基于图卷积神经网络的传递特性约束邻居点的行为,减少了边界离群点和突变点的产生.EchoGPK在大型公开数据集EchoNet-Dynamic上的实验结果表明,左心室分割的Dice分数达92.13%,射血分数预测的MAE达3.92%;方法表现出准确率高、参数量和算力需求低等特点,证明了先验知识在超声医学图像分析中的有效性.展开更多
A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number. We first give a necessary and sufficient condition for a graph G to have circular chromatic number V(G)/α(...A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number. We first give a necessary and sufficient condition for a graph G to have circular chromatic number V(G)/α(G) (where V(G) is the vertex number of G and α(G) is its independence number). From this result, we get a necessary and sufficient condition for a vertex-transitive graph to be star extremal as well as a necessary and sufficient condition for a circulant graph to be star extremal. Using these conditions, we obtain several classes of star extremal graphs.展开更多
A Steinberg-type conjecture on circular coloring is recently proposed that for any prime p≥5,every planar graph of girth p without cycles of length from p+1 to p(p-2)is Cp-colorable(that is,it admits a homomorphism t...A Steinberg-type conjecture on circular coloring is recently proposed that for any prime p≥5,every planar graph of girth p without cycles of length from p+1 to p(p-2)is Cp-colorable(that is,it admits a homomorphism to the odd cycle Cp).The assumption of p≥5 being prime number is necessary,and this conjecture implies a special case of Jaeger’s Conjecture that every planar graph of girth 2p-2 is Cp-colorable for prime p≥5.In this paper,combining our previous results,we show the fractional coloring version of this conjecture is true.Particularly,the p=5 case of our fractional coloring result shows that every planar graph of girth 5 without cycles of length from 6 to 15 admits a homomorphism to the Petersen graph.展开更多
Let h:E(G)→[0,1]be a function.If a≤∑e∋xh(e)≤b holds for each x∈V(G),then we call G[Fh]a fractional[a,b]-factor of G with indicator function h,where Fh={e:e∈E(G),h(e)>0}.A graph G is called a fractional[a,b]-c...Let h:E(G)→[0,1]be a function.If a≤∑e∋xh(e)≤b holds for each x∈V(G),then we call G[Fh]a fractional[a,b]-factor of G with indicator function h,where Fh={e:e∈E(G),h(e)>0}.A graph G is called a fractional[a,b]-covered graph if for every edge e of G,there is a fractional[a,b]-factor G[Fh]with h(e)=1.Zhou,Xu and Sun[S.Zhou,Y.Xu,Z.Sun,Degree conditions for fractional(a,b,k)-critical covered graphs,Information Processing Letters 152(2019)105838]defined the concept of a fractional(a,b,k)-critical covered graph,i.e.,for every vertex subset Q with|Q|=k of G,G−Q is a fractional[a,b]-covered graph.In this article,we study the problem of a fractional(2,b,k)-critical covered graph,and verify that a graph G withδ(G)≥3+k is a fractional(2,b,k)-critical covered graph if its toughness t(G)≥1+1b+k2b,where b and k are two nonnegative integers with b≥2+k2.展开更多
The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. We say a graph G is star extremal if its circular chromatic number is equal to its...The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. We say a graph G is star extremal if its circular chromatic number is equal to its fractional chromatic number. This paper gives an improvement of a theorem. And we show that several classes of circulant graphs are star extremal.展开更多
The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. A graph is called star extremal if its fractional chromatic number equals to its c...The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. A graph is called star extremal if its fractional chromatic number equals to its circular chromatic number (also known as the star chromatic number). This paper studies the star extremality of the circulant graphs whose generating sets are of the form {±1,±k} .展开更多
The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which tw...The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which two vertices x and y are adjacent iff y-x∈D . This paper determines the circular chromatic numbers of two classes of distance graphs G(Z,D m,k,k+1 ) and G(Z,D m,k,k+1,k+2 ).展开更多
The bondage number of γ f, b f(G) , is defined to be the minimum cardinality of a set of edges whose removal from G results in a graph G′ satisfying γ f(G′)> γ f(G) . The reinforcement number of γ f, ...The bondage number of γ f, b f(G) , is defined to be the minimum cardinality of a set of edges whose removal from G results in a graph G′ satisfying γ f(G′)> γ f(G) . The reinforcement number of γ f, r f(G) , is defined to be the minimum cardinality of a set of edges which when added to G results in a graph G′ satisfying γ f(G′)< γ f(G) . G.S.Domke and R.C.Laskar initiated the study of them and gave exact values of b f(G) and r f(G) for some classes of graphs. Exact values of b f(G) and r f(G) for complete multipartite graphs are given and some results are extended.展开更多
基金This work is supported by NNSF of ChinaRFDP of Higher Education
文摘This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.
文摘Let γ f(G) and γ~t f(G) be the fractional domination number and fractional total domination number of a graph G respectively. Hare and Stewart gave some exact fractional domination number of P n×P m (grid graph) with small n and m . But for large n and m , it is difficult to decide the exact fractional domination number. Motivated by this, nearly sharp upper and lower bounds are given to the fractional domination number of grid graphs. Furthermore, upper and lower bounds on the fractional total domination number of strong direct product of graphs are given.
基金the National Natural Science Foundation of China(Nos.12161 and 12031018).
文摘The main contribution in this article is threefold:(1)we show the necessary and sufficient condition for graphs to be fractional(g,f)-covered which can be expressed in different forms,and extended to fractional(g,f,m)-covered graphs;(2)the concept of fractional-critical covered graph is put forward and its necessary and sufficient condition is given;(3)we present the degree condition for a graph to be fractional(g,f,n′,m)-critical covered,and show that degree bound is sharp when m is small.Moreover,the related result in fractional(a,b,n′,m)-critical covered setting is also verified.
文摘The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.
文摘We consider the block matrices and 3-dimensional graph manifolds associated with a special type of tree graphs. We demonstrate that the linking matrices of these graph manifolds coincide with the reduced matrices obtained from the Laplacian block matrices by means of Gauss partial diagonalization procedure described explicitly by W. Neumann. The linking matrix is an important topological invariant of a graph manifold which is possible to interpret as a matrix of coupling constants of gauge interaction in Kaluza-Klein approach, where 3-dimensional graph manifold plays the role of internal space in topological 7-dimensional BF theory. The Gauss-Neumann method gives us a simple algorithm to calculate the linking matrices of graph manifolds and thus the coupling constants matrices.
文摘We present a new algorithm for the fast expansion of rational numbers into continued fractions. This algorithm permits to compute the complete set of integer Euler numbers of the sophisticate tree graph manifolds, which we used to simulate the coupling constant hierarchy for the universe with five fundamental interactions. Moreover, we can explicitly compute the integer Laplacian block matrix associated with any tree plumbing graph. This matrix coincides up to sign with the integer linking matrix (the main topological invariant) of the graph manifold corresponding to the plumbing graph. The need for a special algorithm appeared during computations of these topological invariants of complicated graph manifolds since there emerged a set of special rational numbers (fractions) with huge numerators and denominators;for these rational numbers, the ordinary methods of expansion in continued fraction became unusable.
文摘根据超声心动图准确分析左心室轮廓和射血分数对于心血管疾病诊断意义重大.但现有方法存在左心室分割和射血分数预测之间缺乏关联性、左心室分割关键点易于出现离群点和突变点、方法存储和计算开销大、解释性不佳等问题,为此提出一种基于先验知识引导的轻量级图卷积方法EchoGPK(Echo Guided by Priori Knowledge),以心脏的结构和运动特性、相邻心肌的相似性等先验知识为引导,设计了计算高效的螺旋聚合函数和深度压缩的多头偏心聚合解码器,实现了图卷积结构的轻量化.方法基于临床医生的普遍经验提出了适度利用左心室轮廓的多任务射血分数预测网络,建立了左心室分割和射血分数预测之间的关联性,增强了推理的可解释性;基于图卷积神经网络的传递特性约束邻居点的行为,减少了边界离群点和突变点的产生.EchoGPK在大型公开数据集EchoNet-Dynamic上的实验结果表明,左心室分割的Dice分数达92.13%,射血分数预测的MAE达3.92%;方法表现出准确率高、参数量和算力需求低等特点,证明了先验知识在超声医学图像分析中的有效性.
文摘A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number. We first give a necessary and sufficient condition for a graph G to have circular chromatic number V(G)/α(G) (where V(G) is the vertex number of G and α(G) is its independence number). From this result, we get a necessary and sufficient condition for a vertex-transitive graph to be star extremal as well as a necessary and sufficient condition for a circulant graph to be star extremal. Using these conditions, we obtain several classes of star extremal graphs.
基金partially supported by the National Natural Science Foundation of China(Grant No.11971196)Hubei Provincial Science and Technology Innovation Base(Platform)Special Project 2020DFH002+1 种基金the second author was partially supported by the National Natural Science Foundation of China(Grant Nos.11901318,12131013)the Young Elite Scientists Sponsorship Program by Tianjin(Grant No.TJSQNTJ-2020-09)。
文摘A Steinberg-type conjecture on circular coloring is recently proposed that for any prime p≥5,every planar graph of girth p without cycles of length from p+1 to p(p-2)is Cp-colorable(that is,it admits a homomorphism to the odd cycle Cp).The assumption of p≥5 being prime number is necessary,and this conjecture implies a special case of Jaeger’s Conjecture that every planar graph of girth 2p-2 is Cp-colorable for prime p≥5.In this paper,combining our previous results,we show the fractional coloring version of this conjecture is true.Particularly,the p=5 case of our fractional coloring result shows that every planar graph of girth 5 without cycles of length from 6 to 15 admits a homomorphism to the Petersen graph.
文摘Let h:E(G)→[0,1]be a function.If a≤∑e∋xh(e)≤b holds for each x∈V(G),then we call G[Fh]a fractional[a,b]-factor of G with indicator function h,where Fh={e:e∈E(G),h(e)>0}.A graph G is called a fractional[a,b]-covered graph if for every edge e of G,there is a fractional[a,b]-factor G[Fh]with h(e)=1.Zhou,Xu and Sun[S.Zhou,Y.Xu,Z.Sun,Degree conditions for fractional(a,b,k)-critical covered graphs,Information Processing Letters 152(2019)105838]defined the concept of a fractional(a,b,k)-critical covered graph,i.e.,for every vertex subset Q with|Q|=k of G,G−Q is a fractional[a,b]-covered graph.In this article,we study the problem of a fractional(2,b,k)-critical covered graph,and verify that a graph G withδ(G)≥3+k is a fractional(2,b,k)-critical covered graph if its toughness t(G)≥1+1b+k2b,where b and k are two nonnegative integers with b≥2+k2.
文摘The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. We say a graph G is star extremal if its circular chromatic number is equal to its fractional chromatic number. This paper gives an improvement of a theorem. And we show that several classes of circulant graphs are star extremal.
文摘The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. A graph is called star extremal if its fractional chromatic number equals to its circular chromatic number (also known as the star chromatic number). This paper studies the star extremality of the circulant graphs whose generating sets are of the form {±1,±k} .
文摘The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which two vertices x and y are adjacent iff y-x∈D . This paper determines the circular chromatic numbers of two classes of distance graphs G(Z,D m,k,k+1 ) and G(Z,D m,k,k+1,k+2 ).
文摘The bondage number of γ f, b f(G) , is defined to be the minimum cardinality of a set of edges whose removal from G results in a graph G′ satisfying γ f(G′)> γ f(G) . The reinforcement number of γ f, r f(G) , is defined to be the minimum cardinality of a set of edges which when added to G results in a graph G′ satisfying γ f(G′)< γ f(G) . G.S.Domke and R.C.Laskar initiated the study of them and gave exact values of b f(G) and r f(G) for some classes of graphs. Exact values of b f(G) and r f(G) for complete multipartite graphs are given and some results are extended.
