A lower bound for the tree-width of planar graphs with vital linkages

The disjoint paths problem asks, given an graph G and k + 1 pairs of terminals (s0, t0), . . . , (sk, tk), whether there are k + 1 pairwise disjoint paths P0, . . . , Pk, such that Pi connects si to ti. Robertson and Seymour have proven that the problem can be solved in polynomial time if k is fixed. Nevertheless, the constants involved are huge, and the algorithm is far from implementable. The algorithm uses a bound on the treewidth of graphs with vital linkages, and deletion of irrelevant vertices. We give single exponential lower bounds both for the tree-width of planar graphs with vital linkages, and for the size of the grid necessary for finding irrelevant vertices.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Isolde Adler, Philipp Klaus Krause
• Keywords: Algorithm, Asks, CORR 2010, Education, Polynomial Time