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学者姓名：曾庆厚
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Let F be a family of r-uniform hypergraphs (henceforth r-graphs). An F-saturated r-graph is a maximal r-graph not containing any member of F as a subgraph. For integers l >= r >= 2, let K-l+1(r) be the collection of all r-graphs F with at most ((l+1)(2)) edges such that for some (l+1)-set S every pair {u,v} subset of S is covered by an edge in F, and let T-r(n,l) be the complete l-partite r-graph on n vertices with no two part sizes differing by more than one. Let t(r)(n,l) be the number of edges in T-r(n,l). Our first result shows that for each l >= r >= 2 every K-l+1(r)-saturated r-graph on n vertices with t(r)(n,l)-o(n(r-1+1/l)) edges contains a complete l-partite subgraph on (1-o(1))n vertices, which extends a stability theorem for Kl+1-saturated graphs given by Popielarz, Sahasrabudhe, and Snyder. We also show that the bound is best possible. Our second result is motivated by a celebrated theorem of Andr & aacute;sfai, Erdos, and S & oacute;s, which states that for l >= 2 every Kl+1-free graph G on n vertices with minimum degree delta(G) > 3l-4/3l-1 n is l-partite. We give a hypergraph version of it. The minimum positive co-degree of an r-graph H, denoted by delta(+)(r-1)(H), is the maximum k such that if S is an (r-1)-set contained in an edge of H, then S is contained in at least k distinct edges of H. Let l >= 3 be an integer and H be a K-l+1(3)-saturated 3-graph on n vertices. We prove that if either l >= 4 and delta(+)(2)(H)>3l-7/3l-1 n; or l=3 and delta(+)(2)(H)>2n/7, then H is l-partite; and the bound is best possible. This is the first stability result on minimum positive co-degree for hypergraphs.
Keyword ：
hypergraph hypergraph positive co-degree positive co-degree saturation saturation stability stability
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| GB/T 7714 | Hou, Jianfeng , Li, Heng , Yang, Caihong et al. Two Stability Theorems for Kl+1r-Saturated Hypergraphs [J]. | JOURNAL OF GRAPH THEORY , 2025 . |
| MLA | Hou, Jianfeng et al. "Two Stability Theorems for Kl+1r-Saturated Hypergraphs" . | JOURNAL OF GRAPH THEORY (2025) . |
| APA | Hou, Jianfeng , Li, Heng , Yang, Caihong , Zeng, Qinghou , Zhang, Yixiao . Two Stability Theorems for Kl+1r-Saturated Hypergraphs . | JOURNAL OF GRAPH THEORY , 2025 . |
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The Turan number of a graph H, denoted by ex(n, H), is the maximum number of edges in an n-vertex graph that does not contain H as a subgraph. For a vertex v and a multi-set F of graphs, the suspension F + v of F is the graph obtained by connecting the vertex v to all vertices of F for each F is an element of F. For two integers k 1 and r 2, let Hi be a graph containing a critical edge with chromatic number r for any i is an element of {1, ... , k}, and let H = {H1,. . . , Hk} + v. In this paper, we determine ex(n, H) and characterize all the extremal graphs for sufficiently large n. This generalizes a result of Chen, Gould, Pfender and Wei on intersecting cliques.
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| GB/T 7714 | Hou, Jianfeng , Li, Heng , Zeng, Qinghou . Extremal Graphs for the Suspension of Edge-Critical Graphs [J]. | ELECTRONIC JOURNAL OF COMBINATORICS , 2024 , 20 (4) . |
| MLA | Hou, Jianfeng et al. "Extremal Graphs for the Suspension of Edge-Critical Graphs" . | ELECTRONIC JOURNAL OF COMBINATORICS 20 . 4 (2024) . |
| APA | Hou, Jianfeng , Li, Heng , Zeng, Qinghou . Extremal Graphs for the Suspension of Edge-Critical Graphs . | ELECTRONIC JOURNAL OF COMBINATORICS , 2024 , 20 (4) . |
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In large-scale surveillance of urban or rural areas, an effective placement of cameras is critical in maximizing surveillance coverage or minimizing economic cost of cameras. Existing Surveillance Camera Placement (SCP) methods generally focus on physical coverage of surveillance by implicitly assuming uniform distribution of interested targets or objects across all blocks, which is, however, uncommon in real-world scenarios. In this paper, we are the first to propose a target-aware SCP (tSCP) model, which prioritizes optimizing the task based on uneven target densities, allowing cameras to preferentially cover blocks with more interested targets. First, we define target density as the likelihood of interested targets occurring in a block, which is positively correlated with the importance of the block. Second, we combine aerial imagery with a lightweight object detection network to identify target density. Third, we formulate tSCP as an optimization problem to maximize target coverage in surveillance area, and solve this problem with a target-guided genetic algorithm. Our method optimizes the rational and economical utilization of cameras in large-scale video survillance. Compared with the state-of-the-art methods, our tSCP achieves the highest target coverage with a fixed number of cameras (8.31%-14.81% more than its peers), or utilizes the minimum number of cameras to achieve a preset target coverage. Codes are available at https://github.com/wu-hongxin/tSCP_main.
Keyword ：
Cameras Cameras Internet of Things (IoT) Internet of Things (IoT) large-scale video surveillance large-scale video surveillance Optimization Optimization Robot vision systems Robot vision systems smart city smart city Surveillance camera placement (SCP) Surveillance camera placement (SCP) Task analysis Task analysis Three-dimensional displays Three-dimensional displays Video surveillance Video surveillance Visualization Visualization
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| GB/T 7714 | Wu, Hongxin , Zeng, Qinghou , Guo, Chen et al. Target-Aware Camera Placement for Large-Scale Video Surveillance [J]. | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY , 2024 , 34 (12) : 13338-13348 . |
| MLA | Wu, Hongxin et al. "Target-Aware Camera Placement for Large-Scale Video Surveillance" . | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 34 . 12 (2024) : 13338-13348 . |
| APA | Wu, Hongxin , Zeng, Qinghou , Guo, Chen , Zhao, Tiesong , Chen, Chang Wen . Target-Aware Camera Placement for Large-Scale Video Surveillance . | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY , 2024 , 34 (12) , 13338-13348 . |
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Given two graphs H and F, the maximum possible number of copies of H in an F-free graph on n vertices is denoted by ex(n, H, F). Let l F denote t vertex disjoint copies of F. Gy6ri and Li (2012) obtained results on ex(n, C-3, C2k+1), which was further improved by Alon and Shikhelman (2016). In this paper, we determine the exact value of ex(n, C-3, B C2k+1) and its extremal graph for all l >= 2 and large n. (c) 2024 Elsevier B.V. All rights reserved.
Keyword ：
Cycle Cycle Extremal graph Extremal graph Generalized Tur & aacute;n number Generalized Tur & aacute;n number
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| GB/T 7714 | Hou, Jianfeng , Yang, Caihong , Zeng, Qinghou . Counting triangles in graphs without vertex disjoint odd cycles [J]. | DISCRETE MATHEMATICS , 2024 , 347 (7) . |
| MLA | Hou, Jianfeng et al. "Counting triangles in graphs without vertex disjoint odd cycles" . | DISCRETE MATHEMATICS 347 . 7 (2024) . |
| APA | Hou, Jianfeng , Yang, Caihong , Zeng, Qinghou . Counting triangles in graphs without vertex disjoint odd cycles . | DISCRETE MATHEMATICS , 2024 , 347 (7) . |
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The Tur & aacute;n number of a graph H, ex(n, H), is the maximum number of edges in an n-vertex graph that does not contain H as a subgraph. Let P(k )denote the path on k vertices and let Um of Pki for 1 <= i <= m; in particular, write U-i=1(m) P-ki denote the disjoint union for all 1 <= i <= m. Yuan and Zhang determined ex(n, U-i=1(m) P-ki = mP(k) if k(i) = k i=1 P-ki) for all integers n if at most one of k(1), ... , k(m) is odd. Much less is known for all integers n if at least two of k(1), ... , k(m) are odd. Partial results such as ex(n, mP(3)), ex(n, P-3 boolean OR P2l+1), (n, 2P(5)), ex(n, 2P(7)) and ex(n, 3P(5)) have been established by several researchers. In this paper, we develop new functions and determine ex(n, 3P(7)) and ex(n, 2P(3) boolean OR P2l+1) for all integers n. We also characterize all the extremal graphs. Both results contribute to a conjecture of Yuan and Zhang.
Keyword ：
disjoint paths disjoint paths extremal graph extremal graph Turan number Turan number
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| GB/T 7714 | Deng, Jinghua , Hou, Jianfeng , Zeng, Qinghou . THE TURÁN NUMBER OF THREE DISJOINT PATHS [J]. | DISCUSSIONES MATHEMATICAE GRAPH THEORY , 2023 , 44 (4) : 1513-1537 . |
| MLA | Deng, Jinghua et al. "THE TURÁN NUMBER OF THREE DISJOINT PATHS" . | DISCUSSIONES MATHEMATICAE GRAPH THEORY 44 . 4 (2023) : 1513-1537 . |
| APA | Deng, Jinghua , Hou, Jianfeng , Zeng, Qinghou . THE TURÁN NUMBER OF THREE DISJOINT PATHS . | DISCUSSIONES MATHEMATICAE GRAPH THEORY , 2023 , 44 (4) , 1513-1537 . |
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For any positive integer k, let C(k) denote the least integer such that any n-vertex graph has an induced subgraph with at least n - C(k) vertices, in which at least min{k, n - C(k)} vertices are of the same degree. Caro, Shapira and Yuster initially studied this parameter and showed that S2(k log k) < C(k) < (8k)k. For the first nontrivial case, the authors proved that 3 < C(3) < 6, and the exact value was left as an open problem. In this paper, we first show that 3 < C(3) < 4, improving the former result as well as a recent result of Kogan. For special families of graphs, we prove that C(3) = 3 for K5-free graphs, and C(3) = 1 for large C2s+1-free graphs. In addition, extending a result of Erdos, Fajtlowicz and Staton, we assert that every Kr-free graph is an induced subgraph of a Kr-free graph in which no degree occurs more than three times.(c) 2023 Elsevier B.V. All rights reserved.
Keyword ：
H-free graph H-free graph Induced subgraph Induced subgraph Repeated degree Repeated degree
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| GB/T 7714 | Sun, Gaoxing , Hou, Jianfeng , Zeng, Qinghou . Large induced subgraphs with three repeated degrees [J]. | DISCRETE MATHEMATICS , 2023 , 346 (5) . |
| MLA | Sun, Gaoxing et al. "Large induced subgraphs with three repeated degrees" . | DISCRETE MATHEMATICS 346 . 5 (2023) . |
| APA | Sun, Gaoxing , Hou, Jianfeng , Zeng, Qinghou . Large induced subgraphs with three repeated degrees . | DISCRETE MATHEMATICS , 2023 , 346 (5) . |
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A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two parts differ by at most 1, and its size is the number of edges which go across the two parts. Let C-k be a cycle of length k, and let G be a C-4-free graph with n vertices, m edges and vertex degrees d1, ... , dn. Lin and Zeng proved that if G does not contain C-6 and has a perfect matching, then G admits a bisection of size at least m/2+omega(sigma(n)(i=1) root d(i)). This extends a celebrated bound given by Shearer on Max-Cut of triangle-free graphs. In this paper, we establish a similar result by replacing C-6 with theta (1, 2, 4), theta (2, 3, 3) and theta (3, 3, 3), where theta(l(1), l(2), l(3)) denotes the graph consisting of three internally disjoint paths of length l(1), l(2) and l(3), respectively, each with the same endpoints. We also note that the bound is tight for certain polarity graphs. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
Keyword ：
Bisection Bisection Cycle Cycle Degree Degree theta graph theta graph
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| GB/T 7714 | Rao, Mengjiao , Hou, Jianfeng , Zeng, Qinghou . Maximum bisections of graphs without cycles of length 4 [J]. | DISCRETE MATHEMATICS , 2022 , 345 (8) . |
| MLA | Rao, Mengjiao et al. "Maximum bisections of graphs without cycles of length 4" . | DISCRETE MATHEMATICS 345 . 8 (2022) . |
| APA | Rao, Mengjiao , Hou, Jianfeng , Zeng, Qinghou . Maximum bisections of graphs without cycles of length 4 . | DISCRETE MATHEMATICS , 2022 , 345 (8) . |
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Suppose that G is a graph and H is a subgraph of G. We call H singular if the vertices of H either have the same degree in G or have pairwise distinct degrees in G. Let T-S(n, H) be the largest number of edges of a graph with n vertices that does not contain a singular copy of H. The problem of determining T-S(n, H) was studied initially by Caro and Tuza, who obtained an asymptotic bound for each H. In this paper, we consider the case that H is a star, and determine the exact values of T-S(n, K1,2) for all n, T-S(n, K1,4) and T-S(n, K-1,K-2s+1) for sufficiently large n.
Keyword ：
H-free H-free Singular Singular star star Turan number Turan number
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| GB/T 7714 | Sun, Gaoxing , Li, Heng , Zeng, Qinghou et al. Singular Turan numbers of stars [J]. | PURE AND APPLIED MATHEMATICS QUARTERLY , 2022 , 18 (6) : 2599-2618 . |
| MLA | Sun, Gaoxing et al. "Singular Turan numbers of stars" . | PURE AND APPLIED MATHEMATICS QUARTERLY 18 . 6 (2022) : 2599-2618 . |
| APA | Sun, Gaoxing , Li, Heng , Zeng, Qinghou , Hou, Jianfeng . Singular Turan numbers of stars . | PURE AND APPLIED MATHEMATICS QUARTERLY , 2022 , 18 (6) , 2599-2618 . |
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A long-standing conjecture asserts that there is a positive constant c such that every n-vertex graph without isolated vertices contains an induced subgraph with all degrees odd on at least cn vertices. Recently, Ferber and Krivelevich confirmed the conjecture with c >= 10(-4). However, this is far from optimal for special family of graphs. Scott proved that c >= (2 chi)(-1) for graphs with chromatic number chi >= 2 and conjectured that c >= chi(-1). Partial tight bounds of c are also established by various authors for graphs such as trees, graphs with maximum degree 3 or K-4-minor-free graphs. In this paper, we further prove that c >= 2/5 for planar graphs with girth at least 7, and the bound is tight. We also show that c <= 1/3 for general planar graphs and c >= 1/3 for planar graphs with girth at least 6.
Keyword ：
Girth Girth Induced subgraph Induced subgraph Odd graph Odd graph Planar graph Planar graph
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| GB/T 7714 | Rao, Mengjiao , Hou, Jianfeng , Zeng, Qinghou . Odd Induced Subgraphs in Planar Graphs with Large Girth [J]. | GRAPHS AND COMBINATORICS , 2022 , 38 (4) . |
| MLA | Rao, Mengjiao et al. "Odd Induced Subgraphs in Planar Graphs with Large Girth" . | GRAPHS AND COMBINATORICS 38 . 4 (2022) . |
| APA | Rao, Mengjiao , Hou, Jianfeng , Zeng, Qinghou . Odd Induced Subgraphs in Planar Graphs with Large Girth . | GRAPHS AND COMBINATORICS , 2022 , 38 (4) . |
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Given a graph G, let f(G) denote the maximum number of edges in a bipartite subgraph of G. Given a set .Ye of graphs and a positive integer m, let f (m, .Ye ) denote the minimum possible cardinality of f (G), as G ranges over all graphs on m edges that contains no member of .Ye as a subgraph. Suppose that r >= 10 is an even integer and k >= 2 is an integer. In this paper, we prove that there is a constant c(r) > 0 such that f (m, {C6, C7, ... , Cr & minus;1}) >= m/2 + c(r)mr/(r+1) and there is a constant c(k) > 0 such that f (m, {C4, C6, . . . , C2k, C2k+1}) >= m/2 + c(k)m(2k+2)/(2k+3), both of which improve a result of Alon, Bollob & aacute;s, Krivelevich and Sudakov. (c) 2021 Published by Elsevier B.V. Superscript/Subscript Available</comment
Keyword ：
Bipartite subgraph Bipartite subgraph Forbidden cycle Forbidden cycle Partition Partition
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| GB/T 7714 | Lin, Jing , Zeng, Qinghou . Maximum bipartite subgraphs in graphs without short cycles [J]. | DISCRETE APPLIED MATHEMATICS , 2022 , 311 : 18-25 . |
| MLA | Lin, Jing et al. "Maximum bipartite subgraphs in graphs without short cycles" . | DISCRETE APPLIED MATHEMATICS 311 (2022) : 18-25 . |
| APA | Lin, Jing , Zeng, Qinghou . Maximum bipartite subgraphs in graphs without short cycles . | DISCRETE APPLIED MATHEMATICS , 2022 , 311 , 18-25 . |
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