To reorient is easier than to orient: an on-line algorithm for reorientation of graphs

TL;DR

This paper introduces an online algorithm for reorienting pseudo-transitive graphs into transitive graphs, demonstrating its theoretical implications and computability within formal systems.

Contribution

It presents a novel incremental algorithm for graph reorientation, linking graph theory with formal logic and computability.

Findings

Algorithm successfully reorients pseudo-transitive graphs in an online manner.

Proves Ghouila-Houri's theorem is provable in RCA_0 and is computably true.

Establishes a connection between graph reorientation and formal logical systems.

Abstract

We define an on-line (incremental) algorithm that, given a (possibly infinite) pseudo-transitive oriented graph, produces a transitive reorientation. This implies that a theorem of Ghouila-Houri is provable in RCA_0 and hence is computably true.