Graph Isomorphism for K_{3, 3}-free and K_5-free graphs is in Log-space
نویسندگان
چکیده
Graph isomorphism is an important and widely studied computational problem with a yet unsettled complexity. However, the exact complexity is known for isomorphism of various classes of graphs. Recently, [8] proved that planar isomorphism is complete for log-space. We extend this result further to the classes of graphs which exclude K3,3 or K5 as a minor, and give a log-space algorithm. Our algorithm decomposes K3,3 minor-free graphs into biconnected and those further into triconnected components, which are known to be either planar or K5 components [20]. This gives a triconnected component tree similar to that for planar graphs. An extension of the log-space algorithm of [8] can then be used to decide the isomorphism problem. For K5 minor-free graphs, we consider 3-connected components. These are either planar or isomorphic to the four-rung mobius ladder on 8 vertices or, with a further decomposition, one obtains planar 4-connected components [9]. We give an algorithm to get a unique decomposition of K5 minor-free graphs into bi-, triand 4-connected components, and construct trees, accordingly. Since the algorithm of [8] does not deal with four-connected component trees, it needs to be modified in a quite non-trivial way.
منابع مشابه
Exponential Speedup of Fixed Parameter Algorithms on K_{3,3}-minor-free or K_5-minor-free Graphs
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