Geodesic
A Survey of the Path Partition Conjecture
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 1, pp. 117-131

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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.
Keywords: Path Partition Conjecture, Path Kernel Conjecture, generalized colourings, additive hereditary properties 
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Frick, Marietjie. A Survey of the Path Partition Conjecture. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 1, pp. 117-131. http://geodesic.mathdoc.fr/item/DMGT_2013_33_1_a9/