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}
}
  • M. Frick
  • Published in Discuss. Math. Graph Theory 1 March 2013
  • Mathematics, Computer Science
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. 
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