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学者姓名：侯建锋
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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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For a nondegenerate r-graph F, large n, and t in the regime [0, c(F)n], where c(F)>0 is a constant depending only on F, we present a general approach for determining the maximum number of edges in an n-vertex r-graph that does not contain t+1 vertex-disjoint copies of F. In fact, our method results in a rainbow version of the above result and includes a characterization of the extremal constructions. Our approach applies to many well-studied hypergraphs (including graphs) such as the edge-critical graphs, the Fano plane, the generalized triangles, hypergraph expansions, the expanded triangles, and hypergraph books. Our results extend old results of Erdos [13], Simonovits [76], and Moon [58] on complete graphs, and can be viewed as a step toward a general density version of the classical Corradi-Hajnal [10] and Hajnal-Szemeredi [32] theorems. Our method relies on a novel understanding of the general properties of nondegenerate Turan problems, which we refer to as smoothness and boundedness. These properties are satisfied by a broad class of nondegenerate hypergraphs and appear to be worthy of future exploration.
Keyword ：
F-matching F-matching Hypergraph Turan problems Hypergraph Turan problems stability stability the Corr & aacute;di-Hajnal theorem the Corr & aacute;di-Hajnal theorem vertex-extendability vertex-extendability
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| GB/T 7714 | Hou, Jianfeng , Li, Heng , Liu, Xizhi et al. A step towards a general density Corradi-Hajnal theorem [J]. | CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES , 2025 . |
| MLA | Hou, Jianfeng et al. "A step towards a general density Corradi-Hajnal theorem" . | CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES (2025) . |
| APA | Hou, Jianfeng , Li, Heng , Liu, Xizhi , Yuan, Long-Tu , Zhang, Yixiao . A step towards a general density Corradi-Hajnal theorem . | CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES , 2025 . |
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不同于图的情形,对于正整数r≥3和一些经典的r-一致超图族M,顶点数固定条件下边数最多的不含M的r-一致超图(称为M的极图)可能不止一个,而且这些超图在距离上相距较远,这种现象被称为不稳定性,也是确定此类超图Turán数的基本障碍. Liu和Mubayi (2022)给出了第一个具有不稳定性的3-一致超图族的例子.对于r≥4,通过具有不稳定性的3-一致超图族可以构造具有同样性质的r-一致超图族.本文构造第一个不依赖于3-一致超图的4-一致超图族M,使得M有两个在距离上相距较远的极图.同时,本文证明相应的Andrásfai-Erd?os-Sós型稳定性定理:任意最小度接近于极图平均度的不含M的4-一致超图一定是这两个极图中一个的子图.此外,作为本文结果的推论,本文还证明了M的可行域具有两个最大值点.
Keyword ：
Turán数 Turán数 可行域 可行域 稳定性 稳定性 超图 超图
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| GB/T 7714 | 张一枭 , 李恒 , 侯建锋 . 不具有稳定性质的4-一致超图族 献给刘桂真教授80寿辰 [J]. | 中国科学:数学 , 2024 , 54 (11) : 1905-1924 . |
| MLA | 张一枭 et al. "不具有稳定性质的4-一致超图族 献给刘桂真教授80寿辰" . | 中国科学:数学 54 . 11 (2024) : 1905-1924 . |
| APA | 张一枭 , 李恒 , 侯建锋 . 不具有稳定性质的4-一致超图族 献给刘桂真教授80寿辰 . | 中国科学:数学 , 2024 , 54 (11) , 1905-1924 . |
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Let r >= 2 be an integer. The real number alpha is an element of [0, 1) is a jump for r if there exists a constant c > 0 such that for any & varepsilon; > 0 and any integer m >= r, there exists an integer n(0)(& varepsilon;, m) satisfying any r-uniform graph with n >= n(0) (& varepsilon;, m) vertices and density at least alpha + & varepsilon; contains a subgraph with m vertices and density at least alpha + c. A result of Erdos and Simonovits (1966) and Erdos and Stone (1946) implies that every alpha is an element of [0, 1) is a jump for r = 2. Erdos (1964) asked whether the same is true for r >= 3. Frankl and Rodl (1984) gave a negative answer by showing that 1-1/& ell;(r-1) is not a jump for r if r >= 3 and & ell; > 2r. After that, more non-jumps are found by using a method of Frankl and Rodl (1984). Motivated by an idea of Liu and Pikhurko (2023), in this paper, we show a method to construct maps f: [0, 1) -> [0, 1) that preserve non-jumps, i.e., if alpha is a non-jump for r given by the method of Frankl and Rodl (1984), then f(alpha) is also a non-jump for r. We use these maps to study hypergraph Turan densities and answer a question posed by Grosu (2016).
Keyword ：
hypergraph Lagrangian hypergraph Lagrangian jumping number jumping number non-jump non-jump Turan density Turan density
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| GB/T 7714 | Hou, Jianfeng , Li, Heng , Yang, Caihong et al. Generating non-jumps from a known one [J]. | SCIENCE CHINA-MATHEMATICS , 2024 , 67 (12) : 2899-2908 . |
| MLA | Hou, Jianfeng et al. "Generating non-jumps from a known one" . | SCIENCE CHINA-MATHEMATICS 67 . 12 (2024) : 2899-2908 . |
| APA | Hou, Jianfeng , Li, Heng , Yang, Caihong , Zhang, Yixiao . Generating non-jumps from a known one . | SCIENCE CHINA-MATHEMATICS , 2024 , 67 (12) , 2899-2908 . |
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For many well-known families of triple systems M, there are perhaps many near-extremal M-free configurations that are far from each other in edit-distance. Such a property is called non-stable and is a fundamental barrier to determining the Turan number of M. Liu and Mubayi gave the first finite example that is non-stable. In this paper, we construct another finite family of triple systems M such that there are two near-extremal M-free configurations that are far from each other in edit-distance. We also prove its Andrasfai-Erdos-Sos type stability theorem: Every M-free triple system whose minimum degree is close to the average degree of the extremal configurations is a subgraph of one of these two near-extremal configurations. As a corollary, our main result shows that the boundary of the feasible region of M has exactly two global maxima.
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| GB/T 7714 | Zhang, Yixiao , Hou, Jianfeng , Li, Heng . A 2-stable family of triple systems [J]. | ELECTRONIC JOURNAL OF COMBINATORICS , 2024 , 31 (2) . |
| MLA | Zhang, Yixiao et al. "A 2-stable family of triple systems" . | ELECTRONIC JOURNAL OF COMBINATORICS 31 . 2 (2024) . |
| APA | Zhang, Yixiao , Hou, Jianfeng , Li, Heng . A 2-stable family of triple systems . | ELECTRONIC JOURNAL OF COMBINATORICS , 2024 , 31 (2) . |
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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 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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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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The square G(2) of a graph G is the graph on the same vertex set as G in which two vertices u, v are adjacent if and only if uv is an element of E(G), or u and v have at least one common neighbor in G. We denote by chi 2(G) the chromatic number of G(2), which is the least integer k such that G(2) admits a proper k-coloring. In this paper, we show that if G is a planar graph with maximum degree at most 5, then chi(2)(G) <= 18, which improves a result given by Chen et al. (Discrete Math 345:112766, 2022).
Keyword ：
Chromatic number Chromatic number Planar graph Planar graph Square coloring Square coloring
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| GB/T 7714 | Hou, Jianfeng , Jin, Yindong , Miao, Lianying et al. Coloring Squares of Planar Graphs with Maximum Degree at Most Five [J]. | GRAPHS AND COMBINATORICS , 2023 , 39 (2) . |
| MLA | Hou, Jianfeng et al. "Coloring Squares of Planar Graphs with Maximum Degree at Most Five" . | GRAPHS AND COMBINATORICS 39 . 2 (2023) . |
| APA | Hou, Jianfeng , Jin, Yindong , Miao, Lianying , Zhao, Qian . Coloring Squares of Planar Graphs with Maximum Degree at Most Five . | GRAPHS AND COMBINATORICS , 2023 , 39 (2) . |
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For a graph G and two positive integers t, r, a (t, t + r)-list assignment of G is a function L that assigns a set of permissible colors L(u) to every vertex u such that |L(u) | >= t and |L(u) u L(w) | >= t + r when uw is an edge. The graph G is said to be (t, t + r)-choosable if G allows a proper coloring psi satisfying psi (u) E L(u) for each u E V (G ) and each (t, t + r)-list assignment L of G . In this paper, we consider the (2, 2 + r)-choosability of planar graphs without short cycles. We show that: (1) if G is a planar graph contains no cycles of length 4, then G is (2,9)-choosable; (2) if G is a planar graph contains no cycles of lengths 4 and 5, then G is (2,7)-choosable.(c) 2022 Elsevier Inc. All rights reserved.
Keyword ：
Choosability Choosability C k-free C k-free Discharging Discharging Planar graphs Planar graphs
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| GB/T 7714 | Hou, Jianfeng , Zhu, Hongguo . On (2, r)-choosability of planar graphs without short cycles [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2023 , 444 . |
| MLA | Hou, Jianfeng et al. "On (2, r)-choosability of planar graphs without short cycles" . | APPLIED MATHEMATICS AND COMPUTATION 444 (2023) . |
| APA | Hou, Jianfeng , Zhu, Hongguo . On (2, r)-choosability of planar graphs without short cycles . | APPLIED MATHEMATICS AND COMPUTATION , 2023 , 444 . |
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