Related papers: Problem collection from the IML programme: Graphs,…

In this arxiv-post I present my solutions (published or not) to Problems that appeared in Amer. Math. Monthly, Math. Magazine, Elemente der Mathematik and CRUX, that were mostly done in collaboration with Rudolf Rupp. Some of them…

Recent work has shown the capability of Large Language Models (LLMs) to solve tasks related to Knowledge Graphs, such as Knowledge Graph Completion, even in Zero- or Few-Shot paradigms. However, they are known to hallucinate answers, or…

We suggest a reduction of the combinatorial problem of hypergraph partitioning to a continuous optimization problem.

Recent advancements in Large Language Models (LLMs) have showcased striking results on existing logical reasoning benchmarks, with some models even surpassing human performance. However, the true depth of their competencies and robustness…

Multiple choice questions (MCQs) are a popular method for evaluating students' knowledge due to their efficiency in administration and grading. Crafting high-quality math MCQs is a labor-intensive process that requires educators to…

A probabilistic model for random hypergraphs is introduced to represent unary, binary and higher order interactions among objects in real-world problems. This model is an extension of the Latent Class Analysis model, which captures…

Large language models (LLMs) such as GPT-4 have emerged as frontrunners, showcasing unparalleled prowess in diverse applications, including answering queries, code generation, and more. Parallelly, graph-structured data, an intrinsic data…

Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This generalizes existing results, such as the enumeration of graphs…

Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…

We present ControlLLM, a novel framework that enables large language models (LLMs) to utilize multi-modal tools for solving complex real-world tasks. Despite the remarkable performance of LLMs, they still struggle with tool invocation due…

The Graph Burning Problem (GBP) is a combinatorial optimization problem that has gained relevance as a tool for quantifying a graph's vulnerability to contagion. Although it is based on a very simple propagation model, its decision version…

We present a novel approach to generating mathematical conjectures using Large Language Models (LLMs). Focusing on the solubilizer, a relatively recent construct in group theory, we demonstrate how LLMs such as ChatGPT, Gemini, and Claude…

Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a…

We show that large language models (LLMs) are remarkably good at working with interpretable models that decompose complex outcomes into univariate graph-represented components. By adopting a hierarchical approach to reasoning, LLMs can…

Property graphs are widely used in domains such as healthcare, finance, and social networks, but they often contain errors due to inconsistencies, missing data, or schema violations. Traditional rule-based and heuristic-driven graph repair…

Augmenting specialised machine learning techniques into traditional graph learning models has achieved notable success across various domains, including federated graph learning, dynamic graph learning, and graph transformers. However, the…

Large Language Models (LLMs) are increasingly used for tasks involving Knowledge Graphs (KGs), whose evaluation typically focuses on accuracy and output correctness. We propose a complementary task characterization approach using three…

The integration of large language models (LLMs) with graph-structured data has become a pivotal and fast evolving research frontier, drawing strong interest from both academia and industry. The 2nd LLM+Graph Workshop, co-located with the…

Large Language Models (LLMs) are increasingly being adopted as tools for learning; however, most tools remain text-only, limiting their usefulness for domains where visualizations are essential, such as mathematics. Recent work shows that…

It is known that context-free grammars can be extended to generating graphs resulting in graph grammars; one of such fundamental approaches is hyperedge replacement grammars. On the other hand there are type-logical grammars which also…