An Application of Stahl’s Conjecture About the k-tuple Chromatic Numbers of Kneser Graphs
نویسندگان
چکیده
A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G so that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G is the smallest t so that there is such a k-tuple coloring of G using t colors in all. The Kneser graph K(m,n) has as vertices all n-element subsets of the set {1,2, . . . ,m} and an edge between two subsets iff they are disjoint. The value of the k-tuple chromatic number of the Kneser Graph is the subject of a 30-year-old conjecture of Saul Stahl. This paper summarizes known results about Stahl’s Conjecture and applies the ideas to answer two questions of N.V.R. Mahadev about the relation between the n-tuple chromatic number of a graph and n times the size of its largest clique.
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