Year: 2024
Type: article
Abstract: The Kneser graph $K(n,d)$ is the graph on the $d$-subsets of an $n$-set, adjacent when disjoint. Clearly, $K(n+d,d)$ is locally $K(n,d)$. Hall showed for $n \ge 3d+1$ that there are no further examples. Here we give other examples of locally $K(n,d)$ graphs for $n = 3d$, and some further sporadic examples. It follows that Hall's bound is best possible.
DOI: 10.37236/12621
Author: Andries Brouwer
Institution: University of Amsterdam
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403924839