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EJC
2007

Quickly deciding minor-closed parameters in general graphs

9 years 11 months ago
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...
Erik D. Demaine, Mohammad Taghi Hajiaghayi
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where EJC
Authors Erik D. Demaine, Mohammad Taghi Hajiaghayi
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