TL;DR
This paper introduces a unifying framework called abstract separation systems for studying separations in graphs, matroids, and other structures, and characterizes when these systems can be represented as graph or set separations.
Contribution
It provides a characterization of abstract separation systems that can be represented as separations of graphs, sets, or bipartitions, unifying various combinatorial concepts.
Findings
Characterization of representable separation systems
Unified framework for graph and matroid separations
Conditions for representation as graph or set separations
Abstract
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as separation systems of graphs, sets, or set bipartitions.
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