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pro vyhledávání: '"Long, Tu"'
We determine the maximum number of a graph without containing the 2-power of a Hamilton path. Using this result, we establish a spectral condition for a graph containing the 2-power of a Hamilton path.
Externí odkaz:
http://arxiv.org/abs/2403.05040
Autor:
Ma, Jie, Yuan, Long-Tu
The supersaturation problem for a given graph $F$ asks for the minimum number $h_F(n,q)$ of copies of $F$ in an $n$-vertex graph with $ex(n,F)+q$ edges. Subsequent works by Rademacher, Erd\H{o}s, and Lov\'{a}sz and Simonovits determine the optimal ra
Externí odkaz:
http://arxiv.org/abs/2310.08081
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
Externí odkaz:
http://arxiv.org/abs/2302.09849
The Erd\H{o}s-Simonovits stability theorem is one of the most widely used theorems in extremal graph theory. We obtain an Erd\H{o}s-Simonovits type stability theorem in multi-partite graphs. Different from the Erd\H{o}s-Simonovits stability theorem,
Externí odkaz:
http://arxiv.org/abs/2208.13995
Autor:
Ning, Bo, Yuan, Long-tu
In this paper, we study the stability result of a well-known theorem of Bondy. We prove that for any 2-connected non-hamiltonian graph, if every vertex except for at most one vertex has degree at least $k$, then it contains a cycle of length at least
Externí odkaz:
http://arxiv.org/abs/2207.13650
Autor:
Chi, Cheng, Yuan, Long-Tu
The edge blow-up of a graph is the graph obtained from replacing each edge of it by a clique of the same size where the new vertices of the cliques are all different. Wang, Hou, Liu and Ma determined the Tur\'{a}n number of the edge blow-up of trees
Externí odkaz:
http://arxiv.org/abs/2206.05162
Autor:
Yang, Jia-Bao, Yuan, Long-Tu
Publikováno v:
In Discrete Applied Mathematics 30 October 2024 356:343-349
Autor:
Long, Tu, Zhang, Xifei, Chen, Ding, Gu, Huazhi, Zhang, Meijie, Huang, Ao, Fu, Lvping, Zou, Yongshun, Li, Libei, Qiu, Wendong
Publikováno v:
In Journal of Alloys and Compounds 25 October 2024 1003
Autor:
Zhang, Xifei, Long, Tu, Chen, Ding, Gu, Huazhi, Zhang, Meijie, Huang, Ao, Fu, Lvping, Zou, Yongshun, Li, Libei, Zhang, Jiaqin, Qiu, Wendong
Publikováno v:
In Ceramics International 15 October 2024 50(20) Part B:38896-38903
The bipartite Tur\'{a}n number of a graph $H$, denoted by $ex(m,n; H)$, is the maximum number of edges in any bipartite graph $G=(X,Y; E)$ with $|X|=m$ and $|Y|=n$ which does not contain $H$ as a subgraph. In this paper, we determined $ex(m,n; F_{\el
Externí odkaz:
http://arxiv.org/abs/2201.00453