Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
On the Chromatic Number of the Square of the Kneser Graph K(2k+1, k)
Graphs and Combinatorics
Computing square roots of trivially perfect and threshold graphs
Discrete Applied Mathematics
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The Kneser graphKG(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 graphSG(n,k) is the subgraph of KG(n,k) induced by all vertices that are 2-stable subsets. The squareG^2 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@l(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) @g(KG^2(2k+1,k))==3 and @g(KG^2(9,4))==4, @g(SG^2(8,3))=8, @l(SG(8,3))=9, @g(SG^2(6,2))=9, and @l(SG(6,2))=8.