Maximal Pivots on Graphs with an Application to Gene Assembly

Abstract

We consider principal pivot transform (pivot) on graphs. We define a natural variant of this operation, called dual pivot, and show that both the kernel and the set of maximally applicable pivots of a graph are invariant under this operation. The result is motivated by and applicable to the theory of gene assembly in ciliates.

modest revision (including different latex style) w.r.t. v2, 16 pages, 5 figures

References in corpus (3)

• Strategies of Loop Recombination in Ciliates
• Pivots, Determinants, and Perfect Matchings of Graphs
• The Fibers and Range of Reduction Graphs in Ciliates

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• Nullity and Loop Complementation for Delta-Matroids
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• Sorting by Reversals and the Theory of 4-Regular Graphs