an:00572455
Zbl 0795.05110
Seymour, P. D.; Thomas, Robin
Graph searching and a min-max theorem for tree-width
EN
J. Comb. Theory, Ser. B 58, No. 1, 22-33 (1993).
00019405
1993
j
05C70 05C05 91A43
graph searching; min-max theorem; tree-decomposition; screens; game; tree-width
Summary: The tree-width of a graph \(G\) is the minimum \(k\) such that \(G\) may be decomposed into a ``tree-structure'' of pieces each with at most \(k+1\) vertices. We prove that this equals the maximum \(k\) such that there is a collection of connected subgraphs, pairwise intersecting or adjacent, such that no set of \(\leq k\) vertices meets all of them. A corollary is an analogue of LaPaugh's ``monotone search'' theorem for cops trapping a roober they can see (LaPaugh's robber was invisible).