Geodesic
Some locally Kneser graphs
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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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
Classification : 05C75, 05E30, 05C10
Mots-clés : Johnson scheme, association scheme, distance regular graphs 
@article{10_37236_12621,
     author = {Andries Brouwer},
     title = {Some locally {Kneser} graphs},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {4},
     doi = {10.37236/12621},
     zbl = {1551.05348},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/12621/}
}
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Andries Brouwer. Some locally Kneser graphs. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12621

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