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学者姓名:陈彬
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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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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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