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A Survey of the Path Partition Conjecture

100%

Frick M.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 1

117-131

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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The directed path partition conjecture

88%

Frick M., van Aardt S., Dlamini G., Dunbar J., Oellermann O.

Discussiones Mathematicae Graph Theory

2005

tom 25

nr 3

331-343

The Directed Path Partition Conjecture is the following: If D is a digraph that contains no path with more than λ vertices then, for every pair (a,b) of positive integers with λ = a+b, there exists a vertex partition (A,B) of D such that no path in D⟨A⟩ has more than a vertices and no path in D⟨B⟩ has more than b vertices. We develop methods for finding the desired partitions for various classes of digraphs.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Frick M.

1 Dlamini G.

1 Dunbar J.

1 Oellermann O.

1 van Aardt S.

1 2013

1 2005

Wyniki wyszukiwania

A Survey of the Path Partition Conjecture

The directed path partition conjecture