Tootfinder

Anti-Ukrainian narratives pushed by the Kremlin as deflection tactics. Ukraine in Flames #603: https://benborges.xyz/2024/04/25/antiukrainian-narratives-pushed.html

U.S. Republicans, following orders from ex-President Donald Trump, are blocking arms deliveries to Ukraine, subjecting troops to “ammo starvation” with immediate, deleterious effects on the battlefield.
After taking Bakhmut and Avdiivka, Russian troops are now trying to press their advantage in the directions of Marinka, Robotyne and Kreminna, according to battlefield observers.
European leaders, despite having become Ukraine’s chief material backers, are failing to fill the ga…

Why the West is losing Ukraine
U.S. Republicans blocking aid. European right-wingers pushing to abandon Kyiv. Ultra-cautious leaders. What is the West’s real strategy?

Stability in Graphs with Matroid Constraints
Fedor V. Fomin, Petr A. Golovach, Tuukka Korhonen, Saket Saurabh
https://arxiv.org/abs/2404.03979 https://

Stability in Graphs with Matroid Constraints
We study the following Independent Stable Set problem. Let G be an undirected graph and M = (V(G),I) be a matroid whose elements are the vertices of G. For an integer k\geq 1, the task is to decide whether G contains a set S\subseteq V(G) of size at least k which is independent (stable) in G and independent in M. This problem generalizes several well-studied algorithmic problems, including Rainbow Independent Set, Rainbow Matching, and Bipartite Matching with Separation. We show that - When t…

Seymour's second neighbourhood conjecture: random graphs and reductions
Alberto Espuny D\'iaz, Ant\'onio Gir\~ao, Bertille Granet, Gal Kronenberg
https://arxiv.org/abs/2403.02842

Seymour's second neighbourhood conjecture: random graphs and reductions
A longstanding conjecture of Seymour states that in every oriented graph there is a vertex whose second outneighbourhood is at least as large as its outneighbourhood. In this short note we show that, for any fixed $p\in[0,1/2)$, a.a.s. every orientation of $G(n,p)$ satisfies Seymour's conjecture (as well as a related conjecture of Sullivan). This improves on a recent result of Botler, Moura and Naia. Moreover, we show that $p=1/2$ is a natural barrier for this problem, in the following sense: f…

Don't you love the feeling when you start doing a homework at 4am but then realize you already did that 3 minute quiz 2 weeks ago

This https://arxiv.org/abs/2308.09334 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Packing Integral Tori in Del Pezzo Surfaces
We extend a packing result of R. Hind and E. Kerman for integral Lagrangian tori in $\mathbb{S}^{2} \times \mathbb{S}^{2}$ to the Del Pezzo surfaces $(\mathbb{D}_{n}, ω_{\mathbb{D}_{n}})$ for $n = 1, \dots, 5$. An integral torus is one whose relative area homomorphism is integer-valued, and we seek a maximal integral packing. By definition, this is a disjoint collection $\{L_{i}\}$ of integral Lagrangian tori with the following property: any other integral Lagrangian torus not in this collecti…