A Blass-Sagan bijection on Eulerian equivalence classes

TL;DR

This paper introduces an algorithmic bijection linking Eulerian equivalence classes of totally cyclic orientations to spanning trees without internal activity edges, extending Blass and Sagan's work.

Contribution

It provides a new algorithmic bijection connecting two combinatorial structures related to graph orientations and spanning trees.

Findings

Establishes a bijection between Eulerian equivalence classes and specific spanning trees.

Extends the work of Blass and Sagan with an explicit algorithm.

Enhances understanding of graph orientation and spanning tree relationships.

Abstract

Following the treatment of Blass and Sagan, we present an algorithmic bijection between the Eulerian equivalence classes of totally cyclic orientations and the spanning trees without internal activity edges for a given graph.