Tootfinder

The maximum number of triangles in $K_{1,s,t}$-free graphs
Asier Calbet, Ritesh Goenka
https://arxiv.org/abs/2508.10611 https://arxiv.org/pdf/2508.10611

The maximum number of triangles in $K_{1,s,t}$-free graphs
We consider the following generalized Turán problem: For $2 \le s \le t$, what is the maximum number of triangles in a $K_{1,s,t}$-free graph on $n$ vertices? The previously best known lower and upper bounds are $Ω(n^2)$ and $o(n^{3-1/s})$, respectively. To the best of our knowledge, all known proofs of the upper bound use the triangle removal lemma. We give a new elementary proof that avoids the use of the triangle removal lemma and improves the upper bound to $O\left(n^{3-1/s}(\log n)^{-1+1…

R2GenKG: Hierarchical Multi-modal Knowledge Graph for LLM-based Radiology Report Generation
Futian Wang, Yuhan Qiao, Xiao Wang, Fuling Wang, Yuxiang Zhang, Dengdi Sun
https://arxiv.org/abs/2508.03426

R2GenKG: Hierarchical Multi-modal Knowledge Graph for LLM-based Radiology Report Generation
X-ray medical report generation is one of the important applications of artificial intelligence in healthcare. With the support of large foundation models, the quality of medical report generation has significantly improved. However, challenges such as hallucination and weak disease diagnostic capability still persist. In this paper, we first construct a large-scale multi-modal medical knowledge graph (termed M3KG) based on the ground truth medical report using the GPT-4o. It contains 2477 enti…

RTQA : Recursive Thinking for Complex Temporal Knowledge Graph Question Answering with Large Language Models
Zhaoyan Gong, Juan Li, Zhiqiang Liu, Lei Liang, Huajun Chen, Wen Zhang
https://arxiv.org/abs/2509.03995

RTQA : Recursive Thinking for Complex Temporal Knowledge Graph Question Answering with Large Language Models
Current temporal knowledge graph question answering (TKGQA) methods primarily focus on implicit temporal constraints, lacking the capability of handling more complex temporal queries, and struggle with limited reasoning abilities and error propagation in decomposition frameworks. We propose RTQA, a novel framework to address these challenges by enhancing reasoning over TKGs without requiring training. Following recursive thinking, RTQA recursively decomposes questions into sub-problems, solves …

Generalize across Homophily and Heterophily: Hybrid Spectral Graph Pre-Training and Prompt Tuning
Haitong Luo, Suhang Wang, Weiyao Zhang, Ruiqi Meng, Xuying Meng, Yujun Zhang
https://arxiv.org/abs/2508.11328

Generalize across Homophily and Heterophily: Hybrid Spectral Graph Pre-Training and Prompt Tuning
Graph ``pre-training and prompt-tuning'' aligns downstream tasks with pre-trained objectives to enable efficient knowledge transfer under limited supervision. However, existing methods rely on homophily-based low-frequency knowledge, failing to handle diverse spectral distributions in real-world graphs with varying homophily. Our theoretical analysis reveals a spectral specificity principle: optimal knowledge transfer requires alignment between pre-trained spectral filters and the intrinsic spe…

Time-optimal Asynchronous Minimal Vertex Covering by Myopic Robots
Saswata Jana, Subhajit Pramanick, Adri Bhattacharya, Partha Sarathi Mandal
https://arxiv.org/abs/2508.14247 ht…

Time-optimal Asynchronous Minimal Vertex Covering by Myopic Robots
In a connected graph with an autonomous robot swarm with limited visibility, it is natural to ask whether the robots can be deployed to certain vertices satisfying a given property using only local knowledge. This paper affirmatively answers the question with a set of \emph{myopic} (finite visibility range) luminous robots with the aim of \emph{filling a minimal vertex cover} (MVC) of a given graph $G = (V, E)$. The graph has special vertices, called \emph{doors}, through which robots enter seq…