Séminaire d'équipe(s) Graphs, ALgorithms and Combinatorics

Finding an odd hole through two vertices of a planar graph in polynomial time
Marcin Kamiński

07 February 2014, 10:00 - 07 February 2014, 11:00 Salle/Bat : 475/PCRI-N
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Activités de recherche : Graph Theory

Résumé :

The problem of deciding, given a graph G and two vertices s
and t, whether there exists an induced cycle of given parity passing
through s and t in G is known to be NP-complete. We show how to solve
the problem in O(|V(G)|^7) time when the input graph is planar. This
answers a question posed by McDiarmid, Reed, Schrijver, and Shepherd
[SWAT 1992]. We use techniques from the theory of graph minors as well
as the theory of perfect graphs. This is joint work with Naomi
Nishimura.