Handle slides for delta-matroids. / Moffatt, Iain; eunice.mphako-banda@wits.ac.za, Eunice.

In: European Journal of Combinatorics, Vol. 59, 01.2017, p. 23-33.

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Abstract

A classic exercise in the topology of surfaces is to show that, using handle slides, every disc-band surface, or 1-vertex ribbon graph, can be put in a canonical form consisting of the connected sum of orientable loops, and either non-orientable loops or pairs of interlaced orientable loops. Motivated by the principle that ribbon graph theory informs delta-matroid theory, we find the delta-matroid analogue of this surface classification. We show that, using a delta-matroid analogue of handle slides, every binary delta-matroid in which the empty set is feasible can be written in a canonical form consisting of the direct sum of the delta-matroids of orientable loops, and either non-orientable loops or pairs of interlaced orientable loops. Our delta-matroid results are compatible with the surface results in the sense that they are their ribbon graphic delta-matroidal analogues.
Original languageEnglish
Pages (from-to)23-33
Number of pages11
JournalEuropean Journal of Combinatorics
Volume59
Early online date30 Jul 2016
DOIs
Publication statusPublished - Jan 2017
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

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