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学者姓名：陈彬
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Abstract ：
Let F be a family of digraphs. A digraph D is F-free if it has no isomorphic copy of any member of F. The Tur & aacute;n number ex(n,F) is the largest number of arcs of F-free digraphs on n vertices. Bermond, Germa, Heydemann and Sotteau in 1980 [Girth in digraphs, J. Graph Theory, 4 (1980), 337-341] determined the Tur & aacute;n number of C-k-free strong digraphs on n vertices for k >= 2, where C-k = {C-2,C-3,... , C-k} and Ci is a directed cycle of length i is an element of {2, 3, ... , k}. In this paper, we determine all Tur & aacute;n number of strong digraphs without t >= 2 triangles, extending the previous result for the case k = 3.
Keyword ：
strong digraph strong digraph triangle triangle Tur & aacute;n number Tur & aacute;n number
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| GB/T 7714 | Chen, Bin . TURAN NUMBER OF STRONG DIGRAPHS FORBIDDEN AT LEAST TWO TRIANGLES [J]. | DISCUSSIONES MATHEMATICAE GRAPH THEORY , 2025 . |
| MLA | Chen, Bin . "TURAN NUMBER OF STRONG DIGRAPHS FORBIDDEN AT LEAST TWO TRIANGLES" . | DISCUSSIONES MATHEMATICAE GRAPH THEORY (2025) . |
| APA | Chen, Bin . TURAN NUMBER OF STRONG DIGRAPHS FORBIDDEN AT LEAST TWO TRIANGLES . | DISCUSSIONES MATHEMATICAE GRAPH THEORY , 2025 . |
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Abstract ：
In this paper, we give two extremal results on vertex disjoint-directed cycles in tournaments and bipartite tournaments. Let q >= 2 $q\ge 2$ and k >= 2 $k\ge 2$ be two integers. The first result is that for every strong tournament D $D$, with a minimum out-degree of at least (q-1)k-1 $(q-1)k-1$ with q >= 3 $q\ge 3$, any k $k$ vertex disjoint-directed cycle, which has a length of at least q $q$ in D $D$, has the same length if and only if q=3,k=2 $q=3,k=2$ and D $D$ is isomorphic to PT7 $P{T}_{7}$. The second result is that for each strong bipartite tournament D $D$, with a minimum out-degree of at least qk-1 $qk-1$ with q $q$ being even, any k $k$ vertex disjoint-directed cycle, each of which has a length of at least 2q $2q$ in D $D$, has the same length if and only if D $D$ is isomorphic to a member of BT(n1,n2,& mldr;,nqk) $BT({n}_{1},{n}_{2},\ldots ,{n}_{qk})$. Our results generalize some results of Tan and of Chen and Chang, and in a sense, extend several results of Bang-Jensen et al. of Ma et al. as well as of Wang et al.
Keyword ：
bipartite tournament bipartite tournament disjoint cycle disjoint cycle tournament tournament
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| GB/T 7714 | Chen, Bin . Extremal Results on Disjoint Cycles in Tournaments and Bipartite Tournaments [J]. | JOURNAL OF GRAPH THEORY , 2025 , 110 (1) : 111-121 . |
| MLA | Chen, Bin . "Extremal Results on Disjoint Cycles in Tournaments and Bipartite Tournaments" . | JOURNAL OF GRAPH THEORY 110 . 1 (2025) : 111-121 . |
| APA | Chen, Bin . Extremal Results on Disjoint Cycles in Tournaments and Bipartite Tournaments . | JOURNAL OF GRAPH THEORY , 2025 , 110 (1) , 111-121 . |
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Let H be a hypergraph with vertex set V(H) and hyperedge set E(H). We call a vertex set R⊆V(H) a transversal if it has a nonempty intersection with every hyperedge of H. The transversal number, denoted by τ(H), is the minimum cardinality of transversals. In 2021, Diao verified that the upper bound of transversal number for any connected 3-uniform hypergraph H is at most 2m+13, that is, τ(H)⩽2m+13, where m is the size of H. Moreover, they gave the necessary and sufficient conditions to reach the upper bound, namely τ(H)=2m+13, if and only if H is a hypertree with a perfect matching. In this paper, we investigate the transversal number of connected k-uniform hypergraphs for k⩾3. We confirm that τ(H)⩽(k-1)m+1k for any k-uniform hypergraph H with size m. Furthermore, we show that τ(H)=(k-1)m+1k if and only if H is a hypertree with a perfect matching, which generalizes the results of Diao. © Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Keyword ：
Operations research Operations research
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| GB/T 7714 | Chen, Zi-An , Chen, Bin . An Upper Bound for the Transversal Number of Connected k-Uniform Hypergraphs [J]. | Journal of the Operations Research Society of China , 2024 , 12 (3) : 829-835 . |
| MLA | Chen, Zi-An 等. "An Upper Bound for the Transversal Number of Connected k-Uniform Hypergraphs" . | Journal of the Operations Research Society of China 12 . 3 (2024) : 829-835 . |
| APA | Chen, Zi-An , Chen, Bin . An Upper Bound for the Transversal Number of Connected k-Uniform Hypergraphs . | Journal of the Operations Research Society of China , 2024 , 12 (3) , 829-835 . |
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