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CSR

2008

Springer

2008

Springer

A function f of a graph is called a complete graph invariant if two given graphs G and H are isomorphic exactly when f(G) = f(H). If additionally, f(G) is a graph isomorphic to G, then f is called a canonical form for graphs. Gurevich [9] proves that any polynomial-time computable complete invariant can be transformed into a polynomialtime computable canonical form. We extend this equivalence to the polylogarithmic-time model of parallel computation for classes of graphs having either bounded rigidity index or small separators. In particular, our results apply to three representative classes of graphs embeddable into a fixed surface, namely, to 3-connected graphs admitting either a polyhedral or a large-edge-width embedding as well as to all embeddable 5-connected graphs. Another application covers graphs with treewidth bounded by a constant k. Since for the latter class of graphs a complete invariant is computable in NC, it follows that graphs of bounded treewidth have a canonical for...

Related Content

Added |
19 Oct 2010 |

Updated |
19 Oct 2010 |

Type |
Conference |

Year |
2008 |

Where |
CSR |

Authors |
Johannes Köbler, Oleg Verbitsky |

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