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Isomorphism of chordal (6, 3) graphs

Isomorphie von chordalen (6, 3) Graphen

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Abstract

A graph is chordal if it contains no chordless cycles of length at least four and (q, t) if no set of at mostq vertices induces more thant paths of length three. It is known that the isomorphism problem is isomorphism complete for chordal graphs and for (6, 3) graphs. We present polynomial methods to determine the automorphism partition and to test isomorphism of graphs which are both chordal and (6, 3). The approach is based on the study of simplicial partitions of chordal graphs. It is proved that for chordal (6, 3) graphs the automorphism partition coincides with the coarsest regular simplicial partition. This yields anO(n+m logn) isomorphism test.

Zusammenfassung

Ein Graph ist chordal, wenn er keine sehnenlosen Kreise der Länge mindestens vier enthält und (q, t), wenn keine Menge von höchstensq Knoten mehr alst Wege der Länge drei induziert. Es ist bekannt, daß das Isomorphieproblem für chordale Graphen und für (6, 3) Graphen Isomorphie-vollständig ist. Wir stellen polynomiale Verfahren vor zur Bestimmung der Automorphiepartition und zum Testen der Isomorphie von Graphen, die sowohl chrodal als auch (6, 3) sind. Der zugang basiert auf dem Studium von simplizialen Partitionen von chordalen Graphen. Es wird gezeigt, daß für chordale (6, 3) Graphen die Automorphiepartition mit der gröbsten regulären simplizialen Partition übereinstimmt. Dies führt zu einemO(n+m logn) isomorphietest.

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  1. Institut für Mathematik, Technische Universität München, D-80290, München, Germany

    L. Babel

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  1. L. Babel
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Babel, L. Isomorphism of chordal (6, 3) graphs. Computing 54, 303–316 (1995). https://doi.org/10.1007/BF02238229

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