Abstract:This work considers the following extension of the tree-depth problem: for a given input graph G and integers k and b, find a rooted forest F of height at most k and width at most b (defined as the maximum number of vertices allowed in a level of F ) such that G is a subgraph of the closure of F . We are interested in the case when G is a line graph of a tree, proving that the problem is N P-hard and obtaining a polynomial-time additive 2b-approximation algorithm. This particular class of graphs received a sig… Show more
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