×

On the diameter of Kneser graphs. (English) Zbl 1100.05030

Authors’ abstract: Let \(n\) and \(k\) be positive integers. The Kneser graph \(K^{2n+k}_n\) is the graph with vertex set \([2n+ k]^n\) and where two \(n\)-subsets \(A,B\in [2n+ k]^n\) are joined by an edge if \(A\cap B= \varnothing\). In this note, we show that the diameter of the Kneser graph \(K^{2n+k}_n\) is equal to \(\lceil(n- 1)/k\rceil+ 1\).

MSC:

05C12 Distance in graphs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Frankl, P.; Füredi, Z., Extremal problems concerning Kneser graphs, J. Combin. Theory Ser. B, 40, 270-284 (1986) · Zbl 0564.05002
[2] Lovasz, L., Kneser’s conjecture, chromatic number and homotopy, J. Combin. Theory Ser. A, 25, 319-324 (1978) · Zbl 0418.05028
[3] Stahl, S., \(n\)-tuple colorings and associated graphs, J. Combin. Theory Ser. B, 20, 185-203 (1976) · Zbl 0293.05115
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.