Abstract
The Path Partition Conjecture (PPC) states that if G is any graph and ( 1, 2) any pair of positive integers such that G has no path with more than 1 + 2 vertices, then there exists a partition (V1,V2) of the vertex set of G such that Vi has no path with more than i 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.
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