Face pairing graphs and 3-manifold enumeration

Burton, Benjamin A. (2004) Face pairing graphs and 3-manifold enumeration. Journal of Knot Theory and Its Ramifications (JKTR), 13 8: 1057-1101. doi:10.1142/S0218216504003627

Author Burton, Benjamin A.
Title Face pairing graphs and 3-manifold enumeration
Journal name Journal of Knot Theory and Its Ramifications (JKTR)   Check publisher's open access policy
ISSN 0218-2165
Publication date 2004-01-01
Year available 2004
Sub-type Article (original research)
DOI 10.1142/S0218216504003627
Volume 13
Issue 8
Start page 1057
End page 1101
Total pages 45
Place of publication Singapore
Publisher World Scientific Publishing Company
Language eng
Subject 01 Mathematical Sciences
0105 Mathematical Physics
Abstract The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal ℙ2-irreducible triangulation. In addition we present constraints upon the combinatorial structure of such a triangulation that can be deduced from its face pairing graph. These results are then applied to the enumeration of closed minimal ℙ2-irreducible 3-manifold triangulations, leading to a significant improvement in the performance of the enumeration algorithm. Results are offered for both orientable and non-orientable triangulations.
Keyword Minimal triangulation
Enumeration algorithm
Face pairing graph
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 15 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 17 times in Scopus Article | Citations
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Created: Fri, 18 Dec 2009, 21:09:22 EST by Macushla Boyle on behalf of Faculty of Science