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Graph Theory pp 101-113 | Cite as

The Path Partition Conjecture

  • Marietjie Frick
  • Jean E. DunbarEmail author
Chapter
Part of the Problem Books in Mathematics book series (PBM)

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.

Notes

Acknowledgement

M. Frick is supported by the National Research Foundation of S.A. Grant 107668.

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Authors and Affiliations

  1. 1.Department of Mathematics and Applied MathematicsUniversity of PretoriaPretoriaSouth Africa
  2. 2.Converse CollegeSpartanburgUSA

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