Even Orientations and Pfaffian graphs
Mari\`en Abreu, Domenico Labbate, Federico Romaniello, John Sheehan
TL;DR
This paper provides a new graph-theoretic characterization of Pfaffian graphs using even orientations, extending previous characterizations and linking combinatorial and algebraic approaches.
Contribution
It introduces a characterization of Pfaffian graphs based on even orientations, generalizing earlier results and connecting combinatorial and algebraic methods.
Findings
Characterization of Pfaffian graphs via even orientations
Extension of Fischer and Little's near bipartite non-Pfaffian graph characterization
Equivalence to Little's algebraic characterization
Abstract
We give a characterization of Pfaffian graphs in terms of even orientations, extending the characterization of near bipartite non--pfaffian graphs by Fischer and Little \cite{FL}. Our graph theoretical characterization is equivalent to the one proved by Little in \cite{L73} (cf. \cite{LR}) using linear algebra arguments.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Computational Geometry and Mesh Generation