The Kneser graph KG(n,k) is the graph whose vertex set consists of all k-subsets of an n-set, and two vertices are adjacent if and only if they are disjoint. The Schrijver graph SG(n,k) is the subgraph of KG(n,k) induced by all vertices that are 2-stable subsets. The square G2 of a graph G is defined on the vertex set of G such that distinct vertices within distance two in G are joined by an edge. The span λ(G) of G is the smallest integer m such that an L(2,1)-labeling of G can be constructed using labels belonging to the set {0,1,…,m}. The following results are established. (1) χ(KG2(2k+1,k))⩽3k+2 for k⩾3 and χ(KG2(9,4))⩽12; (2) χ(SG2(2k+2,k))=λ(SG(2k+2,k))=2k+2 for k⩾4, χ(SG2(8,3))=8, λ(SG(8,3))=9, χ(SG2(6,2))=9, and λ(SG(6,2))=8.