@article{Charbit2012LinearTS,
title={Linear Time Split Decomposition Revisited},
author={Pierre Charbit and Fabien de Montgolfier and Mathieu Raffinot},
journal={SIAM J. Discrete Math.},
year={2012},
volume={26},
pages={499-514}
}

Given a family F of subsets of a ground set V , its orthogonal is defined to be the family of subsets that do not overlap any element of F . Using this tool we revisit the problem of designing a simple linear time algorithm for undirected graph split (also known as 1-join) decomposition.Â