Trivial colors in colorings of Kneser graphs

Trivial colors in colorings of Kneser graphs

We show that any proper coloring of a Kneser graph KGn,k with n−2k+2 colors contains a trivial color class (i.e., a color class consisting of sets that all contain a fixed element), provided n>(2+ε)k2, where ε→0 as k→∞. This bound is essentially tight. This is a consequence of a more general resu...

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Veröffentlicht in:Discrete mathematics 2024-04, Vol.347 (4), p.113869, Article 113869
Hauptverfasser: Kiselev, Sergei, Kupavskii, Andrey
Format: Artikel
Sprache:eng
Schlagworte:
Kneser colorings
Kneser graphs
Non-trivial intersecting families
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Zusammenfassung:We show that any proper coloring of a Kneser graph KGn,k with n−2k+2 colors contains a trivial color class (i.e., a color class consisting of sets that all contain a fixed element), provided n>(2+ε)k2, where ε→0 as k→∞. This bound is essentially tight. This is a consequence of a more general result on the minimum number of non-trivial color classes needed to properly color KGn,k.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2023.113869