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学者姓名：侯远
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Abstract ：
An r-uniform hypergraph is linear if every two edges intersect in at most one vertex. Let Kr+1 be a complete graph with r + 1 vertices. The r-uniform hypergraph K-r+1(+), is obtained from Kr+1 by enlarging each edge of Kr+1 with r - 2 new vertices disjoint from V(Kr+1) such that distinct edges of Kr+1 are enlarged by distinct vertices. Let H be a K-r+1(+)-free linear r-uniform hypergraph with n vertices. In this paper, we prove that when n is sufficiently large, the spectral radius rho(H) of the adjacency tensor of H is no more than n/r, i.e., rho(H) <= n/r with equality if and only if r vertical bar n and H is a transversal design, where the transversal design is the balanced r-partite r-uniform hypergraph such that each pair of vertices from distinct parts is contained in one hyperedge exactly. An immediate corollary of this result is that ex(r)(lin) (n, K-r+1(+)) = n(2)/r(2) for sufficiently large n and r vertical bar n, where ex(r)(lin) (n, K-r+1(+)) is the maximum number of edges of an n-vertex K-r+1(+)-free linear r-uniform hypergraph, i.e., the linear Turan number of K-r+1(+).
Keyword ：
expansion of graphs expansion of graphs extremal problem extremal problem linear hypergraph linear hypergraph spectral radius spectral radius
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| GB/T 7714 | Gao, Guorong , Chang, A. N. , Hou, Yuan . SPECTRAL RADIUS ON LINEAR r-GRAPHS WITHOUT EXPANDED Kr+l* [J]. | SIAM JOURNAL ON DISCRETE MATHEMATICS , 2022 , 36 (2) : 1000-1011 . |
| MLA | Gao, Guorong 等. "SPECTRAL RADIUS ON LINEAR r-GRAPHS WITHOUT EXPANDED Kr+l*" . | SIAM JOURNAL ON DISCRETE MATHEMATICS 36 . 2 (2022) : 1000-1011 . |
| APA | Gao, Guorong , Chang, A. N. , Hou, Yuan . SPECTRAL RADIUS ON LINEAR r-GRAPHS WITHOUT EXPANDED Kr+l* . | SIAM JOURNAL ON DISCRETE MATHEMATICS , 2022 , 36 (2) , 1000-1011 . |
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Abstract ：
Let F be a graph. A hypergraph is called Berge F if it can be obtained by replacing each edge in F by a hyperedge containing it. Given a family of graphs F, we say that a hypergraph H is Berge F-free if for every F epsilon F, the hypergraph H does not contain a Berge F as a subhypergraph. In this paper we investigate on the connections between spectral radius of the adjacency tensor and structural properties of a linear hypergraph. In particular, we obtain a spectral version of Turan-type problems over linear k-uniform hypergraphs by using spectral methods.
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| GB/T 7714 | Hou, Yuan , Chang, An , Cooper, Joshua . Spectral extremal results for hypergraphs [J]. | ELECTRONIC JOURNAL OF COMBINATORICS , 2021 , 28 (3) . |
| MLA | Hou, Yuan 等. "Spectral extremal results for hypergraphs" . | ELECTRONIC JOURNAL OF COMBINATORICS 28 . 3 (2021) . |
| APA | Hou, Yuan , Chang, An , Cooper, Joshua . Spectral extremal results for hypergraphs . | ELECTRONIC JOURNAL OF COMBINATORICS , 2021 , 28 (3) . |
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Abstract ：
离散数学课程是本科高校信息类专业必修课,是计算机科学、大数据、人工智能等专业的基础课之一。本文主要对本科高校离散数学课程进行深入探析,摸索如何在有限课时中培养学生的逻辑思维、抽象思维、建模思维、算法思维,提高学生的学习兴趣和学习能力,从而达到离散数学预期的教学效果。
Keyword ：
建模思维 建模思维 抽象思维 抽象思维 离散数学 离散数学 算法思维 算法思维 逻辑思维 逻辑思维
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| GB/T 7714 | 侯远 . 大数据时代下离散数学教学探析 [J]. | 新课程教学:电子版 , 2020 , (22) : 116-117 . |
| MLA | 侯远 . "大数据时代下离散数学教学探析" . | 新课程教学:电子版 22 (2020) : 116-117 . |
| APA | 侯远 . 大数据时代下离散数学教学探析 . | 新课程教学:电子版 , 2020 , (22) , 116-117 . |
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Abstract ：
In this paper, we define a homogeneous polynomial for a general hypergraph, and establish a remarkable connection between clique number and the homogeneous polynomial of a general hypergraph. For a general hypergraph, we explore some inequality relations among spectral radius, clique number and the homogeneous polynomial. We also give lower and upper bounds on the spectral radius of a general hypergraph in terms of the clique number. (C) 2020 Elsevier Inc. All rights reserved.
Keyword ：
Adjacency tensor Adjacency tensor Clique number Clique number General hypergraph General hypergraph Spectral radius Spectral radius
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| GB/T 7714 | Hou, Yuan , Chang, An , Zhang, Lei . A homogeneous polynomial associated with general hypergraphs and its applications [J]. | LINEAR ALGEBRA AND ITS APPLICATIONS , 2020 , 591 : 72-86 . |
| MLA | Hou, Yuan 等. "A homogeneous polynomial associated with general hypergraphs and its applications" . | LINEAR ALGEBRA AND ITS APPLICATIONS 591 (2020) : 72-86 . |
| APA | Hou, Yuan , Chang, An , Zhang, Lei . A homogeneous polynomial associated with general hypergraphs and its applications . | LINEAR ALGEBRA AND ITS APPLICATIONS , 2020 , 591 , 72-86 . |
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For 0 <=alpha< 1 and ak-uniform hypergraphH, the tensorA(alpha)(H) associated withHis defined asA(alpha)(H) =alpha D(H) + (1- alpha)A(H), whereD(Script capital H) andA(H) are the diagonal tensor of degrees and the adjacency tensor ofH, respectively. The alpha-spectra ofHis the set of all eigenvalues ofA(alpha)(H) and the alpha-spectral radius rho(alpha)(H) is the largest modulus of the elements in the spectrum ofA(alpha)(H). In this paper we define the line graphL(H) of a uniform hypergraphHand prove that rho alpha(H)<= 1 kappa rho alpha(L(H))+1+alpha(Delta-1-delta*k), where Delta and delta* are the maximum degree ofHand the minimum degree ofL(H), respectively. We also generalize some results on alpha-spectra ofG(k,s), which is obtained fromGby blowing up each vertex into ans-set and each edge into ak-set where 1 <= s <= k/2.
Keyword ：
alpha-spectra alpha-spectra Hypergraph Hypergraph line graph line graph power hypergraph power hypergraph tensor tensor
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| GB/T 7714 | Hou, Yuan , Chang, An , Shi, Chao . On the alpha-spectra of Uniform Hypergraphs and Its Associated Graphs [J]. | ACTA MATHEMATICA SINICA-ENGLISH SERIES , 2020 , 36 (7) : 842-850 . |
| MLA | Hou, Yuan 等. "On the alpha-spectra of Uniform Hypergraphs and Its Associated Graphs" . | ACTA MATHEMATICA SINICA-ENGLISH SERIES 36 . 7 (2020) : 842-850 . |
| APA | Hou, Yuan , Chang, An , Shi, Chao . On the alpha-spectra of Uniform Hypergraphs and Its Associated Graphs . | ACTA MATHEMATICA SINICA-ENGLISH SERIES , 2020 , 36 (7) , 842-850 . |
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Abstract ：
A mixed bi-uniform supertree H is a connected and acyclic mixed hypergraph with rank(H) = m, in which each edge contains either s or in vertices. In this paper, we determine the structure of extremal hypergraph with maximal spectral radius in mixed bi-uniform supertrees with given number of edges or vertices.
Keyword ：
Adjacency tensor Adjacency tensor Mixed hypergraph Mixed hypergraph Spectral radius Spectral radius
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| GB/T 7714 | Zhang, Lei , Chang, An , Hou, Yuan . The extremal spectral radius of the mixed bi-uniform supertrees [J]. | ARS COMBINATORIA , 2020 , 151 : 189-201 . |
| MLA | Zhang, Lei 等. "The extremal spectral radius of the mixed bi-uniform supertrees" . | ARS COMBINATORIA 151 (2020) : 189-201 . |
| APA | Zhang, Lei , Chang, An , Hou, Yuan . The extremal spectral radius of the mixed bi-uniform supertrees . | ARS COMBINATORIA , 2020 , 151 , 189-201 . |
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Abstract ：
The k-uniform s-hypertree G = (V,E) is an s-hypergraph, where 1 s k - 1; and there exists a host tree T with vertex set V such that each edge of G induces a connected subtree of T. In this paper, some properties of uniform s-hypertrees are establised, as well as the upper and lower bounds on the largest H-eigenvalue of the adjacency tensor of k-uniform s-hypertrees in terms of the maximal degree Delta. Moreover, we also show that the gap between the maximum and the minimum values of the largest H-eigenvalue of k-uniform s-hypertrees is just Iy(Delta (s/k) ).
Keyword ：
adjacency tensor adjacency tensor hypertree hypertree Largest H-eigenvalue Largest H-eigenvalue spectral radius spectral radius
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| GB/T 7714 | Hou, Yuan , Chang, An , Zhang, Lei . Largest H-eigenvalue of uniform s-hypertrees [J]. | FRONTIERS OF MATHEMATICS IN CHINA , 2018 , 13 (2) : 301-312 . |
| MLA | Hou, Yuan 等. "Largest H-eigenvalue of uniform s-hypertrees" . | FRONTIERS OF MATHEMATICS IN CHINA 13 . 2 (2018) : 301-312 . |
| APA | Hou, Yuan , Chang, An , Zhang, Lei . Largest H-eigenvalue of uniform s-hypertrees . | FRONTIERS OF MATHEMATICS IN CHINA , 2018 , 13 (2) , 301-312 . |
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Keyword ：
hyper-Wiener指标 hyper-Wiener指标 Wiener指标 Wiener指标 欧拉图 欧拉图
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| GB/T 7714 | 侯远 , 陈育栎 , 郑艺容 . 欧拉图的hyper-Wiener指标 [J]. | 高校应用数学学报(A辑) , 2016 , (002) . |
| MLA | 侯远 等. "欧拉图的hyper-Wiener指标" . | 高校应用数学学报(A辑) 002 (2016) . |
| APA | 侯远 , 陈育栎 , 郑艺容 . 欧拉图的hyper-Wiener指标 . | 高校应用数学学报(A辑) , 2016 , (002) . |
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通过对连通图hyper-Wiener指标性质的研究,讨论了u+(2n)中hyper-Wiener指标的最小值,得到了达到最小hyper-Wiener指标的完美匹配单圈图的极图,并提出了关于hyper-Wiener指标的1个猜想.
Keyword ：
hyper-Wiener指标 hyper-Wiener指标 单圈图 单圈图 完美匹配 完美匹配
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| GB/T 7714 | 侯远 , 郑艺容 . 完美匹配单圈图的hyper-Wiener指标 [J]. | 河北大学学报（自然科学版） , 2014 , 34 (2) : 113-117 . |
| MLA | 侯远 等. "完美匹配单圈图的hyper-Wiener指标" . | 河北大学学报（自然科学版） 34 . 2 (2014) : 113-117 . |
| APA | 侯远 , 郑艺容 . 完美匹配单圈图的hyper-Wiener指标 . | 河北大学学报（自然科学版） , 2014 , 34 (2) , 113-117 . |
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令P+(n)表示圈没有公共边的n阶连通图的集合,P+(n,m)表示P+(n)中具有m(m≥1)个极小圈的连通图集合.证明了当n≥6时,P+(n,m)中具有最小度距离的图是花F(n,m),它是m个具有一个公共顶点的三角形并在公共顶点粘上n-1-2m条悬挂边的图;同时证明P+(n)中具有最小度距离的图是F(n,1),它是一个三角形并在一个顶点上粘n-3条悬挂边的图.
Keyword ：
Wiener指数 Wiener指数 图变换 图变换 度距离 度距离 连通图 连通图
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| GB/T 7714 | 侯远 . 连通图的度距离和Wiener指数 [J]. | 福州大学学报（自然科学版） , 2014 , 42 (1) : 12-17 . |
| MLA | 侯远 . "连通图的度距离和Wiener指数" . | 福州大学学报（自然科学版） 42 . 1 (2014) : 12-17 . |
| APA | 侯远 . 连通图的度距离和Wiener指数 . | 福州大学学报（自然科学版） , 2014 , 42 (1) , 12-17 . |
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