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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/14294

Title: Pivots, determinants, and perfect matchings of graphs
Authors: BRIJDER, Robert
Harju, Tero
Hoogeboom, Hendrik Jan
Issue Date: 2012
Abstract: We consider sequences of local and edge complementations on graphs with loops (we allow local complementation only on looped vertices). We recall that these operations together form the matrix operation of principal pivot transform (or pivot) restricted to graphs. This fact is not well known, and as a consequence various special cases of the properties of pivot have been rediscovered multiple times. In this paper we give a gentle overview of various properties of pivot for local and edge complementations on graphs. Moreover, we relate the pivot operation to perfect matchings to obtain a purely graph-theoretical characterization of the effect of sequences of pivot operations. Finally, we show that two of the three operations that make up a formal graph model of the biological process of gene assembly in ciliates together form the matrix operation of Schur complement restricted to graphs. (C) 2012 Elsevier B.V. All rights reserved.
Notes: [Brijder, Robert] Hasselt Univ, Dept WET INF, B-3590 Diepenbeek, Belgium. [Brijder, Robert] Transnatl Univ Limburg, Limburg, Belgium. [Harju, Tero] Univ Turku, Dept Math, FI-20014 Turku, Finland. [Hoogeboom, Hendrik Jan] Leiden Univ, Leiden Inst Adv Comp Sci, NL-2300 RA Leiden, Netherlands. robert.brijder@uhasselt.be
URI: http://hdl.handle.net/1942/14294
DOI: 10.1016/j.tcs.2012.02.031
ISI #: 000308452100008
ISSN: 0304-3975
Category: A1
Type: Journal Contribution
Validation: ecoom, 2013
Appears in Collections: Research publications

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