Maximal Pivots on Graphs with an Application to Gene Assembly

TL;DR

This paper introduces a dual pivot operation on graphs, demonstrating invariance of certain properties and applying it to gene assembly in ciliates, advancing understanding of graph transformations in biological contexts.

Contribution

It defines a dual pivot operation on graphs and proves invariance of kernel and maximal pivots, with applications to gene assembly in ciliates.

Findings

Kernel and maximal pivots are invariant under dual pivot.

Dual pivot operation is a natural variant of principal pivot transform.

Application to gene assembly demonstrates biological relevance.

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.