A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Journal of Algorithms
On Generating Strong Elimination Orderings of Strongly Chordal Graphs
Proceedings of the 18th Conference on Foundations of Software Technology and Theoretical Computer Science
Coloring Powers of Planar Graphs
SIAM Journal on Discrete Mathematics
A bound on the chromatic number of the square of a planar graph
Journal of Combinatorial Theory Series B
Distributed algorithm for the maximal 2-packing in geometric outerplanar graphs
Journal of Parallel and Distributed Computing
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We investigate the clique number, the chromatic number and the inductiveness (or the degeneracy) of the square G2 of an outerplanar graph G, and bound as a function of the maximum degree Δ of G. Our main result is a tight bound of Δ for the inductiveness of the square of any outerplanar graph G, when Δ ≥ τ. This implies that a greedy algorithm yields an optimal coloring of such square graphs, and leads to an exact linear time algorithm that holds for any Δ. We then derive optimal upper bounds on the three parameters for outerplanar graphs of smaller degree Δ