J. V. D. Heuvel

collaborators

3 papers

math.CO2026

2-Factors in Graphs

Jan van den Heuvel, Bjarne Toft

An account of 2-factors in graphs and their history is presented. We give a direct graph-theoretic proof of the 2-Factor Theorem and a new variant of it, and also a new complete ch…

math.CO2025

Triangle-free graphs with the fewest independent sets

Pjotr Buys, Jan van den Heuvel, Ross J. Kang

Given $d > 0$ and a positive integer $n$ , let $G$ be a triangle-free graph on $n$ vertices with average degree $d$ . With an elegant induction, Shearer (1983) tightened a seminal resu…

math.CO2025

Multi-Colouring of Kneser Graphs: Notes on Stahl's Conjecture

Jan van den Heuvel, Xinyi Xu

A (finite, undirected) graph is $(n, k)$ -colourable if we can assign each vertex a $k$ -subset of ${1, 2, \dots, n}$ so that adjacent vertices receive disjoint subsets. We consider t…