A Survey of the Path Partition Conjecture

@inproceedings{Frick2013ASO,
title={A Survey of the Path Partition Conjecture},
author={Marietjie Frick},
booktitle={Discuss. Math. Graph Theory},
year={2013}
}
• M. Frick
• Published in Discuss. Math. Graph Theory 1 March 2013
• Mathematics, Computer Science
Abstract The Path Partition Conjecture (PPC) states that if G is any graph and (λ1, λ2) any pair of positive integers such that G has no path with more than λ1 + λ2 vertices, then there exists a partition (V1, V2) of the vertex set of G such that Vi has no path with more than λi vertices, i = 1, 2. We present a brief history of the PPC, discuss its relation to other conjectures and survey results on the PPC that have appeared in the literature since its first formulation in 1981.
3 Citations
Extended Path Partition Conjecture for Semicomplete and Acyclic Compositions
• Computer Science, Mathematics
ArXiv
• 2021
A conjecture stronger than PPC is introduced using a property first studied by Bang-Jensen, Nielsen and Yeo (2006) and it is shown that the stronger conjecture holds for wide families of acyclic and semicomplete compositions.
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