Geodesic
The chromatic number of the \(q\)-Kneser graph for large \(q\)
Ferdinand Ihringer1
1Ghent University
The electronic journal of combinatorics, Tome 26 (2019) no. 1
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We obtain a new weak Hilton-Milner type result for intersecting families of $k$-spaces in $\mathbb{F}_q^{2k}$, which improves several known results. In particular the chromatic number of the $q$-Kneser graph $qK_{n:k}$ was previously known for $n > 2k$ (except for $n=2k+1$ and $q=2$) or $k < q \log q - q$. Our result determines the chromatic number of $qK_{2k:k}$ for $q \geqslant 5$, so that the only remaining open cases are $(n, k) = (2k, k)$ with $q \in \{ 2, 3, 4 \}$ and $(n, k) = (2k+1, k)$ with $q = 2$.
DOI : 10.37236/7907
Classification : 51E20, 05C69, 05B25, 05D05, 06E30

Ferdinand Ihringer  1

1 Ghent University 
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     author = {Ferdinand Ihringer},
     title = {The chromatic number of the {\(q\)-Kneser} graph for large \(q\)},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {1},
     doi = {10.37236/7907},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/7907/}
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Ferdinand Ihringer. The chromatic number of the \(q\)-Kneser graph for large \(q\). The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/7907

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