Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
On the span in channel assignment problems: bounds, computing and counting
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Coloring Powers of Chordal Graphs
SIAM Journal on Discrete Mathematics
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
Labeling bipartite permutation graphs with a condition at distance two
Discrete Applied Mathematics
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An L(2,1)-coloring, or @l-coloring, of a graph is an assignment of non-negative integers to its vertices such that adjacent vertices get numbers at least two apart, and vertices at distance two get distinct numbers. Given a graph G, @l is the minimum range of colors for which there exists a @l-coloring of G. A conjecture by Griggs and Yeh [J.R. Griggs, R.K. Yeh, Labelling graphs with a condition at distance 2, SIAM Journal on Discrete Mathematics 5 (1992) 586-595] states that @l is at most @D^2, where @D is the maximum degree of a vertex in G. We prove that this conjecture holds for weakly chordal graphs. Furthermore, we improve the known upper bounds for chordal bipartite graphs, and for split graphs.