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学者姓名：常安
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Abstract ：
An r-uniform hypergraph is linear if every two edges intersect in at most one vertex. Given a family of r-uniform hypergraphs F, the linear Turan number ex(r)(lin) (n, F) is the maximum number of edges of a linear r-uniform hypergraph on n vertices that does not contain any member of F as a subhypergraph. For each k >= 3, the linear k-cycle C-k is the 3-uniform linear hypergraph with edges h(1), ... , h(k) such that for every 1 <= i <= k - 1, vertical bar h(i) boolean AND h(i+1)vertical bar = 1, vertical bar h(k) boolean AND h(1)vertical bar =1 and h(i) boolean AND h(j) = phi for all other pairs {i, j}, i not equal j. It is proved by Collier-Cartaino, Graber, Jiang [3] and Ergemlidze, Gyori, Methuku [4] that ex(3)(lin) (n, C-5) = Theta(n(3/2)). In this paper, we strengthen their results by proving that ex(3)(lin) (n, C-5) = 1/3 root 3.n(3/2) + O(n). (C) 2022 Elsevier B.V. All rights reserved.
Keyword ：
Extremal problem Extremal problem Linear 5-cycle Linear 5-cycle Linear hypergraph Linear hypergraph Turan number Turan number
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| GB/T 7714 | Gao, Guorong , Chang, An , Sun, Qi . Asymptotic Turan number for linear 5-cycle in 3-uniform linear hypergraphs [J]. | DISCRETE MATHEMATICS , 2023 , 346 (1) . |
| MLA | Gao, Guorong 等. "Asymptotic Turan number for linear 5-cycle in 3-uniform linear hypergraphs" . | DISCRETE MATHEMATICS 346 . 1 (2023) . |
| APA | Gao, Guorong , Chang, An , Sun, Qi . Asymptotic Turan number for linear 5-cycle in 3-uniform linear hypergraphs . | DISCRETE MATHEMATICS , 2023 , 346 (1) . |
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Let p,q be two positive integers.The 3-graph F(p,q)is obtained from the complete 3-graph K3p by adding q new vertices and p(q2)new edges of the form vxy for which v ∈ V(K3p)and {x,y} are new vertices.It frequently appears in many literatures on the Turán number or Turán density of hypergraphs.In this paper,we first construct a new class of r-graphs which can be regarded as a generalization of the 3-graph F(p,q),and prove that these r-graphs have the same Turán density under some situations.Moreover,we investigate the Turán density of the F(p,q)for small p,q and obtain some new bounds on their Turán densities.
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| GB/T 7714 | An CHANG , Guo-rong GAO . On the Turán Density of Uniform Hypergraphs [J]. | 应用数学学报（英文版） , 2023 , 39 (3) : 638-646 . |
| MLA | An CHANG 等. "On the Turán Density of Uniform Hypergraphs" . | 应用数学学报（英文版） 39 . 3 (2023) : 638-646 . |
| APA | An CHANG , Guo-rong GAO . On the Turán Density of Uniform Hypergraphs . | 应用数学学报（英文版） , 2023 , 39 (3) , 638-646 . |
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Seymour's Second Neighborhood Conjecture (SSNC) asserts that there always exists a vertex v such that the cardinality of its second out-neighborhood is at least as large as its out-neighborhood in every finite oriented graph. For t >= s >= 0, an (s, t)-semi-cycle is an oriented cycle obtained from a directed cycle of length t by reversing exactly s continuous arcs. In this paper, we verify that any oriented graph without (2, 8)-semi -cycle satisfies SSNC. Consequently, we prove that SSNC holds for every oriented graph whose underlying graph has no cycle of length 8. (c) 2023 Elsevier B.V. All rights reserved.
Keyword ：
Oriented graph Oriented graph Seymour's second neighborhood conjecture Seymour's second neighborhood conjecture (st)-semi-cycle (st)-semi-cycle
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| GB/T 7714 | Chen, Bin , Chang, An . A note on Seymour's second neighborhood conjecture [J]. | DISCRETE APPLIED MATHEMATICS , 2023 , 337 : 272-277 . |
| MLA | Chen, Bin 等. "A note on Seymour's second neighborhood conjecture" . | DISCRETE APPLIED MATHEMATICS 337 (2023) : 272-277 . |
| APA | Chen, Bin , Chang, An . A note on Seymour's second neighborhood conjecture . | DISCRETE APPLIED MATHEMATICS , 2023 , 337 , 272-277 . |
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Let p; q be two positive integers. The 3-graph F (p; q) is obtained from the complete 3-graph K-p(3) by adding q new vertices and p(q2) new edges of the form vxy for which v epsilon V (K-p(3)) and fx; yg are new vertices. It frequently appears in many literatures on the Turan number or Turan density of hypergraphs. In this paper, we first construct a new class of r-graphs which can be regarded as a generalization of the 3-graph F (p; q), and prove that these r-graphs have the same Turan density under some situations. Moreover, we investigate the Turan density of the F (p; q) for small p; q and obtain some new bounds on their Turan densities.
Keyword ：
Bound Bound Hypergraph Hypergraph Turan density Turan density
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| GB/T 7714 | Chang, An , Gao, Guo-Rong . On the Turan Density of Uniform Hypergraphs [J]. | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES , 2023 , 39 (3) : 638-646 . |
| MLA | Chang, An 等. "On the Turan Density of Uniform Hypergraphs" . | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 39 . 3 (2023) : 638-646 . |
| APA | Chang, An , Gao, Guo-Rong . On the Turan Density of Uniform Hypergraphs . | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES , 2023 , 39 (3) , 638-646 . |
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A conjecture proposed by Bermond and Thomassen in 1981 states that every digraph with minimum out-degree at least 2k-1 $2k-1$ contains k $k$ vertex disjoint directed cycles for any integer k >= 1 $k\ge 1$, which has received substantial attention. This conjecture has been confirmed for k <= 3 $k\le 3$. In 2014, Lichiardopol raised a very related conjecture that for every integer k >= 2 $k\ge 2$, there exists an integer g(k) $g(k)$ such that every digraph with minimum out-degree at least g(k) $g(k)$ contains k $k$ vertex disjoint directed cycles of different lengths. For a digraph D $D$ and a set of k $k$ vertex disjoint directed cycles C ${\mathscr{C}}$ in D $D$, we denote kappa k(C) ${\kappa }<^>{k}({\mathscr{C}})$ to be the maximum number of directed cycles in C ${\mathscr{C}}$ of distinct lengths. Let kappa k(D)=max{kappa k(C) divide Cis a set ofkvertexdisjoint directed cycles inD} ${\kappa }<^>{k}(D)=\max \{{\kappa }<^>{k}({\mathscr{C}})| {\mathscr{C}}\,\,\text{is a set of}\,\,k\,\text{vertex}\,\text{disjoint directed cycles in}\,\,D\}$. We define kappa k(D)=0 ${\kappa }<^>{k}(D)=0$ if D $D$ has no k $k$ vertex disjoint directed cycles. In this paper, we mainly investigate vertex disjoint directed cycles in tournaments and bipartite tournaments. We first show that kappa k(D)>= 2 ${\kappa }<^>{k}(D)\ge 2$ for every tournament D $D$ with minimum out-degree at least 2k-1 $2k-1$, where k >= 3 $k\ge 3$. We further prove that for k >= 1 $k\ge 1$ and gamma is an element of{1,2, horizontal ellipsis ,k} $\gamma \in \{1,2,\ldots ,k\}$, any tournament D $D$ with minimum out-degree at least gamma 2-2 gamma+6k-32 $\frac{{\gamma }<^>{2}-2\gamma +6k-3}{2}$ satisfies that kappa k(D)>=gamma ${\kappa }<^>{k}(D)\ge \gamma $. Moreover, we deduce that for any tournament D $D$ with minimum out-degree at least 7, kappa 3(D)=3 ${\kappa }<^>{3}(D)=3$ holds. Additionally, we classify strong bipartite tournaments with minimum out-degree at least 2k-1 $2k-1$ in which any k $k$ vertex disjoint directed cycles have the same length, where k >= 2 $k\ge 2$. That is, for any strong bipartite tournament D $D$ with minimum out-degree at least 2k-1 $2k-1$, then kappa k(D)=1 ${\kappa }<^>{k}(D)=1$ if and only if D $D$ is isomorphic to a member of BT(n1,n2, horizontal ellipsis ,n2k) $BT({n}_{1},{n}_{2},\ldots ,{n}_{2k})$, which is defined in the context.
Keyword ：
bipartite tournament bipartite tournament tournament tournament vertex disjoint cycle vertex disjoint cycle
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| GB/T 7714 | Chen, Bin , Chang, An . Disjoint cycles in tournaments and bipartite tournaments [J]. | JOURNAL OF GRAPH THEORY , 2023 , 105 (2) : 297-314 . |
| MLA | Chen, Bin 等. "Disjoint cycles in tournaments and bipartite tournaments" . | JOURNAL OF GRAPH THEORY 105 . 2 (2023) : 297-314 . |
| APA | Chen, Bin , Chang, An . Disjoint cycles in tournaments and bipartite tournaments . | JOURNAL OF GRAPH THEORY , 2023 , 105 (2) , 297-314 . |
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Dankelmann, Guo and Surmacs proved that every bridgeless graph Gof order nwith given maximum degree Delta( G) has an orientation of diameter at most n - Delta(G) + 3[J. Graph Theory, 88(1)(2018), 5-17]. They also constructed a family of bridgeless graphs whose oriented diameter reaches this upper bound. In this paper, we show that Ghas an orientation of diameter at most n - [ g(G)-1/2 ] (Delta(G) - 4) - 1, where g(G) is the girth of G. Moreover, we construct several families of bridgeless graphs whose oriented diameter attains n - [ g(G)-1/2 ] (Delta(G) - 4) - 1, and prove that the upper bound is tight for Delta(G) >= 4. We also give a necessary condition for a bridgeless graph to attain this upper bound. Furthermore, we verify that if Gis a 3-connected graph with girth at least 5, then the oriented diameter of such Gis at most n - [ g(G)-1/2 ] (Delta(G) - 4) - 2.
Keyword ：
Bridgeless graph Bridgeless graph Girth Girth Maximum degree Maximum degree Oriented diameter Oriented diameter
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| GB/T 7714 | Chen, Bin , Chang, An . Oriented diameter of graphs with given girth and maximum degree [J]. | DISCRETE MATHEMATICS , 2022 , 346 (4) . |
| MLA | Chen, Bin 等. "Oriented diameter of graphs with given girth and maximum degree" . | DISCRETE MATHEMATICS 346 . 4 (2022) . |
| APA | Chen, Bin , Chang, An . Oriented diameter of graphs with given girth and maximum degree . | DISCRETE MATHEMATICS , 2022 , 346 (4) . |
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An r-uniform hypergraph is linear if every two edges intersect in at most one vertex. Given a family of r-uniform hypergraphs F, the linear Turan number exlin r (n, F) is the maximum number of edges of a linear r-uniform hypergraph on n vertices that does not contain any member of F as a subgraph. Let Kl be a complete graph with l vertices and r 2. The r-expansion of Kl is the r-graph Kl+ obtained from Kl by enlarging each edge of Kl with a vertex set of size r - 2 disjoint from V(Kl) such that distinct edges of Kl are enlarged by disjoint sets. Let T2(n, l) be the Turan graph, i.e., almost balanced complete l-partite graph with n vertices. When l r 3 and n is sufficiently large, we prove the following extension of Turan's Theorem exlin!n, K+" " |T2(n, l)| r " , l+1 !r 2 with equality holds if and only if there exist almost balanced l-partite r-graphs such that each pair of vertices from distinct parts are contained in one hyperedge exactly. Moreover, some results on linear Turan number of general configurations are also presented.
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| GB/T 7714 | Gao, Guorong , Chang, An . A linear hypergraph extension of Tuan?s Theorem [J]. | ELECTRONIC JOURNAL OF COMBINATORICS , 2022 , 29 (4) : 1-12 . |
| MLA | Gao, Guorong 等. "A linear hypergraph extension of Tuan?s Theorem" . | ELECTRONIC JOURNAL OF COMBINATORICS 29 . 4 (2022) : 1-12 . |
| APA | Gao, Guorong , Chang, An . A linear hypergraph extension of Tuan?s Theorem . | ELECTRONIC JOURNAL OF COMBINATORICS , 2022 , 29 (4) , 1-12 . |
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A digraph D is r-free if such D has no directed cycles of length at most r, where r is a positive integer. In 1980, Bermond et al. showed that if D is an r-free strong digraph of order n, then the size of D is at most ((n-r+2)(2)) + r - 2 and the upper bound is tight, for r >= 2. Namely, they determined the Turan number of C-r-free strong digraphs of order n, where C-r = {C-2, C-3, ..., C-r} and C-i is a directed cycle of length i is an element of {2, 3, ..., r}. Specially, for r = 3, the maximum size of 3-free strong digraphs of order n is ((n-1)(2)) + 1. Let Phi(n)(xi, gamma) be a family of 3-free strong digraphs of order n in which the minimum out-degree is at least xi and the minimum in-degree is at least gamma, where both xi and gamma are positive integers. Let phi(n)(xi, gamma) be the maximum size of digraphs of Phi(n)(xi, gamma), i.e., Turan number of 3-free strong digraphs of order n with out and in-degree restrictions. We denote phi(n)(xi, gamma) = {D is an element of Phi(n)(xi, gamma) : the size of D is equal to phi(n)(xi, gamma)}. Recently, Chen et al. described phi(n)(1, 1), i.e., all 3-free strong digraphs of order n with size ((n-1)(2)) + 1. They also gave the bound of phi(n)(2, 1), that is, ((n-1)(2))-2 <= phi(n)(2, 1) <= ((n-1)(2)). In this paper, we improve the upper bound of phi(n)(2, 1) to ((n-1)(2)) - 1 and we thus get ((n-1)(2)) - 2 <= phi(n)(2, 1) <= ((n-1)(2)) - 1. In addition, we show that phi(n)(2, 1) = ((n-1)(2)) - 1 by constructing two 3-free strong digraphs with minimum out-degree two whose size reaches ((n-1)(2)) - 1 for n = 7, 8, and verify phi(n)(2, 1) = ((n-1)(2)) - 2 for n = 9. As a consequence, Turan number of 3-free strong digraphs of order n with out-degree at least two, i.e., phi(n)(2, 1), is one of ((n-1)(2)) - 1 and ((n-1)(2)) - 2. (C) 2022 Elsevier B.V. All rights reserved.
Keyword ：
3-free strong digraph 3-free strong digraph Out-degree Out-degree Turan number Turan number
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| GB/T 7714 | Chen, Bin , Chang, An . Turan number of 3-free strong digraphs with out-degree restriction [J]. | DISCRETE APPLIED MATHEMATICS , 2022 , 314 : 252-264 . |
| MLA | Chen, Bin 等. "Turan number of 3-free strong digraphs with out-degree restriction" . | DISCRETE APPLIED MATHEMATICS 314 (2022) : 252-264 . |
| APA | Chen, Bin , Chang, An . Turan number of 3-free strong digraphs with out-degree restriction . | DISCRETE APPLIED MATHEMATICS , 2022 , 314 , 252-264 . |
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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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Bermond et al in 1980 proved that if the size of a strong digraph D of order n is at least ((n - k + 2) (2)) + k - 1, k >= 2, then the girth of D is no more than k. Consequently, when D is a 3-free strong digraph of order n without loops or parallel arcs, which means that every directed cycle in D has length at least 4, the maximum size of D is ((n - 1) (2)) + 1. In 2008, Seymour et al proved that if D is a 3-free digraph, then beta(D) <= gamma(D), and they further conjectured that beta(D) <= 1/2 gamma(D) for every 3-free digraph D, where beta(D)denotes the size of the smallest subset X subset of A(D), such that D\X is acyclic, and gamma(D) is the number of unordered pairs {u, v} of vertices such that u, v are nonadjacent in D. In this paper, we first describe all 3-free strong digraphs of order n with the maximum size ((n - 1) (2)) + 1. Then we prove that such 3-free strong digraphs satisfy the minimum out-degree of D equals 1 and beta(D) <= 1/2 gamma(D). Moreover, we prove that if the minimum out-degree of a 3-free strong digraph D is at least 2, then the maximum size of D is between ((n - 1) (2)) - 2 and ((n - 1) (2)).
Keyword ：
3-free digraph 3-free digraph Maximum size Maximum size Minimum out-degree Minimum out-degree Strong digraph Strong digraph
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| GB/T 7714 | Chen, Bin , Chang, An . 3-Free Strong Digraphs with the Maximum Size [J]. | GRAPHS AND COMBINATORICS , 2021 , 37 (6) : 2535-2554 . |
| MLA | Chen, Bin 等. "3-Free Strong Digraphs with the Maximum Size" . | GRAPHS AND COMBINATORICS 37 . 6 (2021) : 2535-2554 . |
| APA | Chen, Bin , Chang, An . 3-Free Strong Digraphs with the Maximum Size . | GRAPHS AND COMBINATORICS , 2021 , 37 (6) , 2535-2554 . |
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