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It is well-known that Brualdi-Hoffman-Tur\'an-type problem asks what is the maximum spectral radius $\lambda(G)$ of an $F$-free graph $G$ with $m$ edges? It can be viewed as a spectral characterization on the existence of the subgraph $F$ in $G.$ A n
Externí odkaz:
http://arxiv.org/abs/2409.15918
Autor:
Zhou, Zihan, Li, Shuchao
Given a graph $G,$ a subset of vertices is called a maximum dissociation set of $G$ if it induces a subgraph with vertex degree at most 1, and the subset has maximum cardinality. The cardinality of a maximum dissociation set is called the dissociatio
Externí odkaz:
http://arxiv.org/abs/2403.18522
Autor:
Yao, Fanglong, Tian, Changyuan, Liu, Jintao, Zhang, Zequn, Liu, Qing, Jin, Li, Li, Shuchao, Li, Xiaoyu, Sun, Xian
Reasoning ability is one of the most crucial capabilities of a foundation model, signifying its capacity to address complex reasoning tasks. Chain-of-Thought (CoT) technique is widely regarded as one of the effective methods for enhancing the reasoni
Externí odkaz:
http://arxiv.org/abs/2308.06207
A graph $G$ is said to be $k$-extendable if every matching of size $k$ in $G$ can be extended to a perfect matching of $G$, where $k$ is a positive integer. We say $G$ is $1$-excludable if for every edge $e$ of $G$, there exists a perfect matching ex
Externí odkaz:
http://arxiv.org/abs/2304.12565
Let $\mathcal{F}$ denote a set of graphs. A graph $G$ is said to be $\mathcal{F}$-free if it does not contain any element of $\mathcal{F}$ as a subgraph. The Tur\'an number is the maximum possible number of edges in an $\mathcal{F}$-free graph with $
Externí odkaz:
http://arxiv.org/abs/2206.09295
Given a graph $G$, the adjacency matrix and degree diagonal matrix of $G$ are denoted by $A(G)$ and $D(G)$, respectively. In 2017, Nikiforov \cite{0007} proposed the $A_{\alpha}$-matrix: $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G),$ where $\alpha\in [0
Externí odkaz:
http://arxiv.org/abs/2204.08301
Publikováno v:
In Discrete Mathematics October 2024 347(10)
Autor:
Li, Shuchao, Zhou, Zihan
Publikováno v:
In Applied Mathematics and Computation 1 January 2025 484
Autor:
Li, Shuchao, Yu, Yuantian
Publikováno v:
In Discrete Mathematics November 2024 347(11)
It is well known that spectral Tur\'{a}n type problem is one of the most classical {problems} in graph theory. In this paper, we consider the spectral Tur\'{a}n type problem. Let $G$ be a graph and let $\mathcal{G}$ be a set of graphs, we say $G$ is
Externí odkaz:
http://arxiv.org/abs/2109.04599