# 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} }

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, MathematicsArXiv
- 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.

My Top 10 Graph Theory Conjectures and Open Problems

- Mathematics
- 2016

This paper presents brief discussions of ten of my favorite, well-known, and not so well-known conjectures and open problems in graph theory, including (1) the 1963 Vizing’s Conjecture about the…

The Path Partition Conjecture is True and its Validity Yields Upper Bounds for Detour Chromatic Number and Star Chromatic Number

- Mathematics
- 2014

The detour order of a graph $G$, denoted $\tau(G)$, is the order of a longest path in $G$. A partition $(A, B)$ of $V(G)$ such that $\tau(\langle A \rangle) \leq a$ and $\tau(\langle B \rangle) \leq…

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