On the chromatic number of q-Kneser graphs

A. Blokhuis; A.E. Brouwer; T.I. Szonyi

doi:10.1007/s10623-011-9513-1

On the chromatic number of q-Kneser graphs

A. Blokhuis, A.E. Brouwer, T.I. Szonyi

Discrete Algebra and Geometry

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Abstract

We show that the q-Kneser graph $qK_{2k:k}$ (the graph on the k-subspaces of a 2k-space over GF(q), where two k-spaces are adjacent when they intersect trivially), has chromatic number $q^k + q^{k-1}$ for k = 3 and for k <q log q - q. We obtain detailed results on maximal cocliques for k = 3. Keywords: Chromatic number – q-analog of Kneser graph

Original language	English
Pages (from-to)	187-197
Journal	Designs, Codes and Cryptography
Volume	65
Issue number	3
DOIs	https://doi.org/10.1007/s10623-011-9513-1
Publication status	Published - 2012

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T1 - On the chromatic number of q-Kneser graphs

AU - Blokhuis, A.

AU - Brouwer, A.E.

AU - Szonyi, T.I.

PY - 2012

Y1 - 2012

N2 - We show that the q-Kneser graph $qK_{2k:k}$ (the graph on the k-subspaces of a 2k-space over GF(q), where two k-spaces are adjacent when they intersect trivially), has chromatic number $q^k + q^{k-1}$ for k = 3 and for k <q log q - q. We obtain detailed results on maximal cocliques for k = 3. Keywords: Chromatic number – q-analog of Kneser graph

AB - We show that the q-Kneser graph $qK_{2k:k}$ (the graph on the k-subspaces of a 2k-space over GF(q), where two k-spaces are adjacent when they intersect trivially), has chromatic number $q^k + q^{k-1}$ for k = 3 and for k <q log q - q. We obtain detailed results on maximal cocliques for k = 3. Keywords: Chromatic number – q-analog of Kneser graph

U2 - 10.1007/s10623-011-9513-1

DO - 10.1007/s10623-011-9513-1

M3 - Article

VL - 65

SP - 187

EP - 197

JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

SN - 0925-1022

IS - 3

ER -

On the chromatic number of q-Kneser graphs

Abstract

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