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

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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.
Classification : 05C15, 05C38, 05C70
Mots-clés : Path Partition Conjecture, Path Kernel Conjecture, generalized colourings, additive hereditary properties, path partition conjecture, path kernel conjecture 
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Marietjie Frick. A Survey of the Path Partition Conjecture. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 1, p. 117. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_1_267737/