The list distinguishing number of Kneser graphs

Abstract

A graph G is said to be k-distinguishable if every vertex of the graph can be colored from a set of k colors such that no non-trivial automorphism fixes every color class. The distinguishing number D(G) is the least integer k for which G is k-distinguishable. If for each v∈V(G) we have a list L(v) of colors, and we stipulate that the color assigned to vertex v comes from its list L(v) then G is said to be L-distinguishable where L={L(v)}v∈V(G). The list distinguishing number of a graph, denoted Dl(G), is the minimum integer k such that every collection of lists L with |L(v)|=k admits an L-distinguishing coloring. In this paper, we prove that Dl(G)=D(G) when G is a Kneser graph.