Kneser's Conjecture

By E. Weisstein. 2002

266 citations recorded by the source corpus.

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On the chromatic number of Kneser hypergraphs (2002, background): “Erdős’ generalization of Kneser’s conjecture to hypergraphs, dealing with the chromatic number of KGr( ( [n] k ) ), was established by Alon, Frankl, and Lovász [1].”
Topology and combinatorics of partitions of masses by hyperplanes (2003, unknown): “Lovasz, [25]), “splitting necklace problem” (N.”
Proof of the Lovász conjecture (2004, methodology): “The actual theorem from [15] is stated using the neighborhood complexes N (H).”
Topological lower bounds for the chromatic number: A hierarchy (2002, methodology): “In 1978 Lovász [22] settled Kneser’s conjecture by an original application of a tool from”
Partitions of nonzero elements of a finite field into pairs (2010, background): “bounds for the chromatic number of the Kneser graphs in [17], other examples of topological methods can be found in [18, 24].”
Extremal problems for cycles in graphs (2016, background): “Since dim(W ) + dim(W⊥) ≤ dim(V ), we conclude dim(W ) ≤ 2 which implies Pi = Pj for some i 6= j (see [86] for details).”
Proof of the middle levels conjecture (2014, background): “the so-called Kneser graphs and bipartite Kneser graphs, only the denser ones are known to have a Hamilton cycle [Che03, SS04, Joh11] (Kneser graphs were introduced by Lovász in his celebrated proof of Kneser’s conjecture [Lov78]).”