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pro vyhledávání: '"Yan Zilong"'
Erd\H{o}s and Simonovits asked the following question: For an integer $c\geq 2$ and a family of graphs $\mathcal{F}$, what is the infimum of $\alpha$ such that any $\mathcal{F}$-free $n$-vertex graph with minimum degree at least $\alpha n$ has chroma
Externí odkaz:
http://arxiv.org/abs/2409.03407
Autor:
Yan, Zilong, Peng, Yuejian
F\"uredi and Gunderson showed that $ex(n, C_{2k+1})$ is achieved only on $K_{\lfloor\frac{n}{2}\rfloor, \lceil\frac{n}{2}\rceil}$ if $n\ge 4k-2$. It is natural to study how far a $ C_{2k+1}$-free graph is from being bipartite.Let $T^*(r, n)$ be obtai
Externí odkaz:
http://arxiv.org/abs/2408.15487
In the rapid development of artificial intelligence, solving complex AI tasks is a crucial technology in intelligent mobile networks. Despite the good performance of specialized AI models in intelligent mobile networks, they are unable to handle comp
Externí odkaz:
http://arxiv.org/abs/2310.09049
Autor:
Yan, Zilong, Peng, Yuejian
The Lagrangian density of an $r$-uniform hypergraph $H$ is $r!$ multiplying the supremum of the Lagrangians of all $H$-free $r$-uniform hypergraphs. For an $r$-uniform graph $H$ with $t$ vertices, it is clear that $\pi_{\lambda}(H)\ge r!\lambda{(K_{t
Externí odkaz:
http://arxiv.org/abs/2209.13250
Autor:
Li, Zhihao, Ding, Zhuang, Yan, Zilong, Han, Konghao, Zhang, Maofeng, Zhou, Hongyang, Sun, Xu, Sun, Hui, Li, Jianhua, Zhang, Wei, Liu, Xiaohong
Publikováno v:
In Talanta 1 January 2025 281
Autor:
Yan, Zilong, Peng, Yuejian
Given bipartite graphs $H_1$, \dots , $H_k$, the bipartite Ramsey number $br(H_1,\dots, H_k)$ is the minimum integer $N$ such that any $k$-edge-coloring of complete bipartite graph $K_{N, N}$ contains a monochromatic $H_i$ in color $i$ for $1\le i\le
Externí odkaz:
http://arxiv.org/abs/2112.14960
Autor:
Yan, Zilong, Peng, Yuejian
We say that a graph $F$ can be embedded into a graph $G$ if $G$ contains an isomorphic copy of $F$ as a subgraph. Guo and Volkmann \cite{GV} conjectured that if $G$ is a connected graph with at least $n$ vertices and minimum degree at least $n-3$, th
Externí odkaz:
http://arxiv.org/abs/2112.14955
Autor:
Yan, Zilong, Peng, Yuejian
A real number $\alpha\in [0, 1)$ is a jump for an integer $r\ge 2$ if there exists $c>0$ such that no number in $(\alpha , \alpha + c)$ can be the Tur\'an density of a family of $r$-uniform graphs. A classical result of Erd\H os and Stone \cite{ES} i
Externí odkaz:
http://arxiv.org/abs/2112.14943
Autor:
Yan, Zilong, Peng, Yuejian
The {\em Tur\'an number} of an $r$-uniform graph $F$, denoted by $ex(n,F)$, is the maximum number of edges in an $F$-free $r$-uniform graph on $n$ vertices. The {\em Tur\'{a}n density} of $F$ is defined as $\pi(F)=\underset{{n\rightarrow\infty}}{\lim
Externí odkaz:
http://arxiv.org/abs/2112.14935