A Kneser graph is a type of graph in mathematics, specifically in graph theory. It is constructed from a set of subsets of a finite set. For a given positive integers n and k , the vertices of the Kneser graph K(n, k) represent the k -element subsets of an n -element set. Two vertices are connected by an edge if the corresponding subsets are disjoint. Kneser graphs are notable for their applications in combinatorics and topology. They are also linked to the Lovász theorem, which states that the chromatic number of a Kneser graph is equal to n - 2k + 2 . This property makes Kneser graphs an important subject of study in discrete mathematics.