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Let $\cal H$ be a family of graphs. The Tur\'an number ${\rm ex}(n,{\cal H})$ is the maximum possible number of edges in an $n$-vertex graph which does not contain any member of $\cal H$ as a subgraph. As a common generalization of Tur\'an's theorem
Externí odkaz:
http://arxiv.org/abs/2410.06449
Let $p,q$ be two integers with $p\geq q$. Given a finite graph $F$ with no isolated vertices, the generalized Ramsey achievement game of $F$ on the complete graph $K_n$, denoted by $(p,q;K_n,F,+)$, is played by two players called Alice and Bob. In ea
Externí odkaz:
http://arxiv.org/abs/2408.01479
Given a graph $T$ and a family of graphs $\mathcal{F}$, the maximum number of copies of $T$ in an $\mathcal{F}$-free graph on $n$ vertices is called the generalized Tur\'{a}n number, denoted by $ex(n, T , \mathcal{F})$. When $T= K_2$, it reduces to t
Externí odkaz:
http://arxiv.org/abs/2406.17371
Autor:
Ye, Chuang-Chao, An, Ning-Bo, Ma, Teng-Yang, Dou, Meng-Han, Bai, Wen, Chen, Zhao-Yun, Guo, Guo-Ping
Great progress has been made in quantum computing in recent years, providing opportunities to overcome computation resource poverty in many scientific computations like computational fluid dynamics (CFD). In this work, efforts are made to exploit qua
Externí odkaz:
http://arxiv.org/abs/2406.16595
Autor:
Lin, Feng-Li, Ning, Bo
Inspired by the recent discovery of a violation of strong cosmic censorship (SCC) for the near-extremal Reissner-Nordstr\"om black holes in de Sitter space (RN-dS), we investigate if the weak cosmic censorship conjecture (WCCC) can also be violated i
Externí odkaz:
http://arxiv.org/abs/2405.07728
Let $G$ be a graph on $n$ vertices with degree sequence $(d_1,d_2......d_n)$. For a real $p \geq 1$, let $D_p(G)=\sum_{i=1}^nd_i^p$. A Tur\'an-type problem of degree power sum was initiated by Caro and Yuster \cite{caro2000degpower}: determining the
Externí odkaz:
http://arxiv.org/abs/2404.07059
In 2002, Nikiforov proved that for an $n$-vertex graph $G$ with clique number $\omega$ and edge number $m$, the spectral radius $\lambda(G)$ satisfies $\lambda (G) \leq \sqrt{2(1 - 1/\omega) m}$, which confirmed a conjecture implicitly suggested by E
Externí odkaz:
http://arxiv.org/abs/2312.16138
Let $G$ be a connected graph and $\mathcal{P}(G)$ a graph parameter. We say that $\mathcal{P}(G)$ is feasible if $\mathcal{P}(G)$ satisfies the following properties: (I) $\mathcal{P}(G)\leq \mathcal{P}(G_{uv})$, if $G_{uv}=G[u\to v]$ for any $u,v$, w
Externí odkaz:
http://arxiv.org/abs/2312.08226
Let $F$ be a graph and $\SPEX (n, F)$ be the class of $n$-vertex graphs which attain the maximum spectral radius and contain no $F$ as a subgraph. Let $\EX (n, F)$ be the family of $n$-vertex graphs which contain maximum number of edges and no $F$ as
Externí odkaz:
http://arxiv.org/abs/2307.14629