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A fundamental result in extremal graph theory attributes to Mantel's theorem, which states that every graph on $n$ vertices with more than $\lfloor n^2/4 \rfloor$ edges contains a triangle. About half of a century ago, Lov\'{a}sz and Simonovits (1975
Externí odkaz:
http://arxiv.org/abs/2408.01709
Recently, Ning and Zhai (2023) proved that every $n$-vertex graph $G$ with $\lambda (G) \ge \sqrt{\lfloor n^2/4\rfloor}$ has at least $\lfloor n/2\rfloor -1$ triangles, unless $G=K_{\lceil \frac{n}{2} \rceil, \lfloor \frac{n}{2} \rfloor}$. The aim of
Externí odkaz:
http://arxiv.org/abs/2407.04950
A well-known theorem of Mantel states that every $n$-vertex graph with more than $\lfloor n^2/4\rfloor $ edges contains a triangle. An interesting problem in extremal graph theory studies the minimum number of edges contained in triangles among graph
Externí odkaz:
http://arxiv.org/abs/2406.13176
Publikováno v:
Advances in Applied Mathematics 158 (2024) 102720
A classical result of Erd\H{o}s and Rademacher (1955) indicates a supersaturation phenomenon. It says that if $G$ is a graph on $n$ vertices with at least $\lfloor {n^2}/{4} \rfloor +1$ edges, then $G$ contains at least $\lfloor {n}/{2}\rfloor$ trian
Externí odkaz:
http://arxiv.org/abs/2406.05609
High-entropy alloys (HEAs) and their corresponding high-entropy hydrides are new potential candidates for negative electrode materials of nickel-metal hydride (Ni-MH) batteries. This study investigates the cyclic electrochemical hydrogen storage perf
Externí odkaz:
http://arxiv.org/abs/2405.06115
A well-known result of Nosal states that a graph $G$ with $m$ edges and $\lambda(G) > \sqrt{m}$ contains a triangle. Nikiforov [Combin. Probab. Comput. 11 (2002)] extended this result to cliques by showing that if $\lambda (G) > \sqrt{2m(1-1/r)}$, th
Externí odkaz:
http://arxiv.org/abs/2404.03423
In this paper, we derive a tight upper bound for the size of an intersecting $k$-Sperner family of subspaces of the $n$-dimensional vector space $\mathbb{F}_{q}^{n}$ over finite field $\mathbb{F}_{q}$ which gives a $q$-analogue of the Erd\H{o}s' $k$-
Externí odkaz:
http://arxiv.org/abs/2403.04289
Publikováno v:
Electron. J. Combin. 31 (1) (2024), #P1.52
A theorem of Nosal and Nikiforov states that if $G$ is a triangle-free graph with $m$ edges, then $\lambda (G)\le \sqrt{m}$, where the equality holds if and only if $G$ is a complete bipartite graph. A well-known spectral conjecture of Bollob\'{a}s a
Externí odkaz:
http://arxiv.org/abs/2304.00716
The Tur\'an number $\mathrm{ex}(n,H)$ of a graph $H$ is the maximum number of edges in an $n$-vertex graph which does not contain $H$ as a subgraph. The Tur\'{a}n number of regular polyhedrons was widely studied in a series of works due to Simonovits
Externí odkaz:
http://arxiv.org/abs/2302.03278
Let $F_s$ be the friendship graph obtained from $s$ triangles by sharing a common vertex. For fixed $s\ge 2$ and sufficiently large $n$, the $F_s$-free graphs of order $n$ which attain the maximal spectral radius was firstly characterized by Cioab\u{
Externí odkaz:
http://arxiv.org/abs/2301.06008