On the chromatic number of q-Kneser graphs
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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.
KeywordsChromatic number q-analog of Kneser graph
Mathematics Subject Classification (2000)51E20 05B25 05D99
Author A. Blokhuis acknowledges support from ERC grant DISCRETECONT 227701. This research began when T. Szőnyi was visiting Eindhoven University of Technology. The hospitality of TU/e and the financial support of EIDMA and Lex Schrijver’s Spinoza grant is gratefully acknowledged. Later T. Szőnyi was partly supported by OTKA Grant K 81310. In Spring 2004 the first author visited Günther Ziegler in Berlin. One of the problems he suggested to look at was determining the chromatic number of the q-Kneser graph.
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