Tootfinder

Graphs Excluding a Minor in Blowups of Treewidth 3 Graphs
Marc Distel
https://arxiv.org/abs/2510.09063 https://arxiv.org/pdf/2510.09063

Graphs Excluding a Minor in Blowups of Treewidth 3 Graphs
Alon, Seymour, and Thomas [J. Amer. Math. Soc. 1990] famously showed that every $n$-vertex $K_h$-minor-free graph has treewidth $O_h(\sqrt{n})$. Recently, Distel, Dujmović, Eppstein, Hickingbotham, Joret, Micek, Morin, Seweryn, and Wood [SIAM J. Discrete Math. 2024] refined this by showing that these graphs are $O_h(\sqrt{n})$-blowups of treewidth $4$ graphs. We improve this by showing that these graphs are $O_h(\sqrt{n})$-blowups of treewidth $3$ graphs.

DualResearch: Entropy-Gated Dual-Graph Retrieval for Answer Reconstruction
Jinxin Shi, Zongsheng Cao, Runmin Ma, Yusong Hu, Jie Zhou, Xin Li, Lei Bai, Liang He, Bo Zhang
https://arxiv.org/abs/2510.08959

DualResearch: Entropy-Gated Dual-Graph Retrieval for Answer Reconstruction
The deep-research framework orchestrates external tools to perform complex, multi-step scientific reasoning that exceeds the native limits of a single large language model. However, it still suffers from context pollution, weak evidentiary support, and brittle execution paths. To address these issues, we propose DualResearch, a retrieval and fusion framework that matches the epistemic structure of tool-intensive reasoning by jointly modeling two complementary graphs: a breadth semantic graph th…

Project-Level C-to-Rust Translation via Synergistic Integration of Knowledge Graphs and Large Language Models
Zhiqiang Yuan, Wenjun Mao, Zhuo Chen, Xiyue Shang, Chong Wang, Yiling Lou, Xin Peng
https://arxiv.org/abs/2510.10956

Project-Level C-to-Rust Translation via Synergistic Integration of Knowledge Graphs and Large Language Models
Translating C code into safe Rust is an effective way to ensure its memory safety. Compared to rule-based translation which produces Rust code that remains largely unsafe, LLM-based methods can generate more idiomatic and safer Rust code because LLMs have been trained on vast amount of human-written idiomatic code. Although promising, existing LLM-based methods still struggle with project-level C-to-Rust translation. They typically partition a C project into smaller units (\eg{} functions) base…

On Stable Cutsets in General and Minimum Degree Constrained Graphs
Mats Vroon, Hans L. Bodlaender
https://arxiv.org/abs/2510.09432 https://arxiv.org/pdf/25…

On Stable Cutsets in General and Minimum Degree Constrained Graphs
A stable cutset is a set of vertices $S$ of a connected graph, that is pairwise non-adjacent and when deleting $S$, the graph becomes disconnected. Determining the existence of a stable cutset in a graph is known to be NP-complete. In this paper, we introduce a new exact algorithm for Stable Cutset. By branching on graph configurations and using the $O^*(1.3645)$ algorithm for the (3,2)-Constraint Satisfaction Problem presented by Beigel and Eppstein, we achieve an improved running time of $O^*…

Pairs of tree dessins, their Shabat polynomials, and monodromy groups
Benjamin Dupont, Revekka Kyriakoglou, Vassilis Metaftsis, Efstratios Prassidis, Alexandros Singh
https://arxiv.org/abs/2510.10192

Pairs of tree dessins, their Shabat polynomials, and monodromy groups
Coverings of the Riemann sphere by itself, ramified over two points, are given by so-called Shabat polynomials. The correspondence between Grothendieck's dessins d'enfants and Belyi maps then implies a bijection between Shabat polynomials and tree dessins (bicolored plane trees). Dessins can be assigned a combinatorial invariant known as their passport, which records the degrees of their vertices. We consider all possible passports determining a pair of tree dessins, determining the associated …

Petition of Right, (1628)
was a petition sent by the English Parliament to King Charles I,
complaining of a series of breaches of law.
The petition sought recognition of four principles:
🔸no taxation without the consent of Parliament,
🔸no imprisonment without cause,
🔸no quartering of soldiers on subjects,
🔸and no martial law in peacetime.
After dismissing his second Parliament,
Charles imposed a "forced loan", an effective tax wh…

A geometric obstruction to self-simulation for groups
Sebasti\'an Barbieri, Kan\'eda Blot, Mathieu Sablik, Ville Salo
https://arxiv.org/abs/2510.10291 https://

A geometric obstruction to self-simulation for groups
We introduce a new quasi-isometry invariant for finitely generated groups and show that every group with this property admits a subshift which is effectively closed by patterns and that cannot be realized as the topological factor of any subshift of finite type. We provide several examples of groups with the property, such as amenable groups, multi-ended groups, generalized Baumslag-Solitar groups, fundamental groups of surfaces, and cocompact Fuchsian groups.