A set $B$ of vertices in a graph $G$ is called a \emph{$k$-limited packing} if for each vertex $v$ of $G$, its closed neighbourhood has at most $k$ vertices in $B$. The \emph{$k$-limited packing number} of a graph $G$, denoted by $L_k(G)$, is the lar...
The k-limited packing number, $L_k(G)$, of a graph $G$, introduced by Gallant, Gunther, Hartnell, and Rall, is the maximum cardinality of a set $X$ of vertices of $G$ such that every vertex of $G$ has at most $k$ elements of $X$ in its closed neighbo...
Let $f^{(r)}(n;s,k)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph containing no subgraph with $k$ edges and at most $s$ vertices. Brown, Erdős and Sós [New directions in the theory of graphs (Proc. Third Ann Arbor Conf...
Let $G$ be a finite group and $\text{cd}(G)$ denote the character degree set for $G$. The prime graph $Δ(G)$ is a simple graph whose vertex set consists of prime divisors of elements in $\text{cd}(G)$, denoted $ρ(G)$. Two primes $p,q\in ρ(G)$ are...
In this paper we introduce the symmetric normaliser graph of a group $G$. The vertex set of this graph consists of elements of the group. Vertices $x$ and $y$ are adjacent if $x$ lies in the normaliser of $\langle y \rangle$ and $y$ lies in the norma...
Based on elastic collisions, the linear momentum of a fast neutron can be measured from as few as two consecutive recoil ion tracks plus the vertex position of the third collision, or `two and half' ion tracks. If the time delay between the first two...
In this paper, we introduce GraphLake, a purpose-built graph compute engine for Lakehouse. GraphLake is built on top of the commercial graph database TigerGraph. It maps Lakehouse tables to vertex and edge types in a labeled property graph and suppor...
Let G be an input graph with n vertices and m edges and let k be a fixed parameter. We provide a single exponential FPT algorithm with running time O(c^kn(n+m)), c= min {18,k} that turns graph G into an interval graph by deleting at most k vertices f...
We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We demonstrate the p...
An efficient algorithm is presented to compute the characteristic polynomial of a threshold graph. Threshold graphs were introduced by Chvátal and Hammer, as well as by Henderson and Zalcstein in 1977. A threshold graph is obtained from a one vertex...
We propose a DBI vertex brane + $N_c$ fundamental strings configuration for a probe baryon in the finite-temperature thermal gauge field via AdS/CFT correspondence. In particular, we investigate properties of this configuration in QCD_4 and warped...
Alon, Seymour and Thomas [1990] proved that every $n$-vertex graph excluding $K_t$ as a minor has treewidth less than $t^{3/2}\sqrt{n}$. Illingworth, Scott and Wood [2022] recently refined this result by showing that every such graph is a subgraph of...
Let $P$ be a set of $n$ points in strictly convex position in the plane. Let $D_n$ be the graph whose vertex set is the set of all line segments with endpoints in $P$, where disjoint segments are adjacent. The chromatic number of this graph was first...
The physics program of high energy e+e- linear colliders relies on the accurate identification of fermions to study in details the profile of the Higgs boson, search for new particles and later probe the multi-TeV mass region by direct searches and...
A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey, Titterington and Tor...
Complement-reducible graphs (or cographs) are the graphs formed from the single-vertex graph by the operations of complement and disjoint union. By combining the Johnson-Newman theorem on generalized cospectrality with the standard tools in the asymp...
We study a market of investments on networks, where each agent (vertex) can invest in any enterprise linked to her, and at the same time, raise capital for her firm's enterprise from other agents she is linked to. Failing to raise sufficient capital...
今天，我们在 Google AI Studio 和 Vertex AI 上发布了更新版本的 Gemini 2.5 Flash 和 2.5 Flash-… 显示全部
为什么谷歌是世界上最伟大的公司 算算谷歌爹送了我多少钱： 先说实打实的， 1.vertex ai 的300刀赠金（gcp） 2.两个账号的GeminiPro（中国大学的邮箱居然也他妈的可以领，这就是我谷歌爹的格局）， …
多平台可用：Anthropic API、亚马逊 Bedrock、谷歌云 Vertex AI 均已上线。 Claude 4 Opus：最强编程模型 「我们已经有一段时间没有 Opus 模型了，」Dario 在发布会上提醒道，「Opus 是我们能力最 …