Path decompositions of digraphs

Author:

Alspach Brian R.,Pullman Norman J.

Abstract

A path decomposition of a digraph G (having no loops or multiple arcs) is a family of simple paths such that every arc of G lies on precisely one of the paths of the family. The path number, pn(G) is the minimal number of paths necessary to form a path decomposition of G.We show that pn(G) ≥ max{0, od(v)-id(v)} the sum taken over all vertices v of G, with equality holding if G is acyclic. If G is a subgraph of a tournament on n vertices we show that pn(G) ≤ with equality holding if G is transitive.We conjecture that pn(G) ≤ for any digraph G on n vertices if n is sufficiently large, perhaps for all n ≥ 4.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 16 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Path decompositions of tournaments;Proceedings of the London Mathematical Society;2023-01-19

2. Path Decompositions of Tournaments;Trends in Mathematics;2021

3. Decomposing tournaments into paths;Proceedings of the London Mathematical Society;2020-04-29

4. An Annotated Glossary of Graph Theory Parameters, with Conjectures;Graph Theory;2018

5. Decomposing tournaments into paths;Electronic Notes in Discrete Mathematics;2017-08

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