One-to-one disjoint path covers in digraphs with faulty edges

Ruixiao Jing and Yuefang Sun

Applied Mathematics and Computation, 2025, vol. 493, issue C

Abstract: Let D be a digraph of order n≥l+1, where l is a positive integer. Let S={s} and T={t}. A set of l paths {P1,P2,…,Pl} of D is a one-to-one l-disjoint directed path cover (one-to-one l-DDPC for short) for S and T, if ⋃i=1lV(Pi)=V(D), each Pi is an s−t path and V(Pi)∩V(Pj)={s,t} for i≠j. If there is a one-to-one l-DDPC in D for any disjoint source set S={s} and sink set T={t}, then D is one-to-one l-coverable. In this paper, we study one-to-one disjoint path covers in digraphs with faulty edges.

Keywords: Complete digraph; Complete bipartite digraph; Faulty edge; One-to-one; Minimum semi-degree (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:493:y:2025:i:c:s0096300324007318

DOI: 10.1016/j.amc.2024.129270

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