Quickly deciding minor-closed parameters in general graphs

We construct algorithms for deciding essentially any minor-closed parameter, with explicit time bounds. This result strengthens previous results by Robertson and Seymour [1,2], Frick and Grohe [3], and Fellows and Langston [4] toward obtaining fixed-parameter algorithms for a general class of parameters. 1 Motivation A major result from the seminal Graph Minors series of papers (in particular [1,2]) is that every minor-closed graph property is characterized by a finite set of forbidden minors. More precisely, for any property P on graphs such that a graph having property P implies that all its minors have property P, there is a finite set {H1, H2, . . . , Hh} of graphs such that a graph G has property P if and only if G does not have Hi as a minor for all i = 1, 2, . . . , h. The algorithmic consequence of this result is that there exists an O(n3 )-time algorithm to decide any fixed minorclosed graph property, by finitely many calls to an O(n3 )-time minor test [1]. This conseque...

• Type: Journal
• Year: 2007
• Where: EJC
• Authors: Erik D. Demaine, Mohammad Taghi Hajiaghayi
• Keywords: Algorithms, EJC 2007, Graph Property, Information Technology, Parameters