The Fibers and Range of Reduction Graphs in Ciliates

TL;DR

This paper explores the structure of reduction graphs in ciliate gene assembly, characterizing which legal strings produce identical graphs and identifying which graphs can be realized as reduction graphs.

Contribution

It provides a complete characterization of legal strings with identical reduction graphs and identifies which graphs are realizable as reduction graphs in gene assembly.

Findings

Legal strings with the same reduction graph are fully characterized.

A characterization of graphs that are isomorphic to reduction graphs is provided.

Insights into the structure of gene assembly processes in ciliates.

Abstract

The biological process of gene assembly has been modeled based on three types of string rewriting rules, called string pointer rules, defined on so-called legal strings. It has been shown that reduction graphs, graphs that are based on the notion of breakpoint graph in the theory of sorting by reversal, for legal strings provide valuable insights into the gene assembly process. We characterize which legal strings obtain the same reduction graph (up to isomorphism), and moreover we characterize which graphs are (isomorphic to) reduction graphs.