Strong orientation of a connected graph for a crossing family

Abdi, Ahmad ORCID: 0000-0002-3008-4167, Dalirrooyfarda, Mahsa and Neuwohner, Meike ORCID: 0000-0002-3664-3687 (2025) Strong orientation of a connected graph for a crossing family. Operations Research Letters. ISSN 0167-6377 (In Press)

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Abstract

Given a connected graph G = (V,E) and a crossing family C over ground set V such that |δG(U)| ≥ 2 for every U ∈ C, we prove there exists a strong orientation of G for C, i.e., an orientation of G such that each set in C has at least one outgoing and at least one incoming arc. This implies the main conjecture in Chudnovsky et al. (Disjoint dijoins. Journal of Combinatorial Theory, Series B, 120:18–35, 2016).

Item Type:	Article
Additional Information:	© 2025 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	08 Apr 2025 14:09
Last Modified:	09 May 2025 20:08
URI:	http://eprints.lse.ac.uk/id/eprint/127859

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