Abstract
The Path Partition Conjecture (PPC) states that if G is any graph and (a, b) any pair of positive integers such that G has no path with more than a + b vertices, then there exists a partition (A, B) of the vertex set of G such that A has no path with more than a vertices, and B has no path with more than b vertices. We present a brief history of the PPC, discuss its relation to other conjectures and examine results supporting the PPC that have appeared in the literature since its first formulation in 1981. We conclude with a few related open problems.
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