The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace

Thomas Thierauf (1) , Fabian Wagner (2)

1 Fakultät Elektronik und Informatik
2 Institut für Theoretische Informatik

The isomorphism problem for planar graphs is known to be efficiently solvable. For planar 3-connected graphs, the isomorphism problem can be solved by efficient parallel algorithms, it is in the class $AC^1$. In this paper we improve the upper bound for planar 3-connected graphs to unambiguous logspace, in fact to $UL \cap coUL$. As a consequence of our method we get that the isomorphism problem for oriented graphs is in $NL$. We also show that the problems are hard for $L$.

Domaines: Algorithme et structure de données [cs.DS]; Complexité [cs.CC]

Thomas Thierauf, Fabian Wagner. The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace. STACS 2008, Feb 2008, Bordeaux, France. pp.633-644. ⟨hal-00255966⟩