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The directed path partition conjecture

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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

1 Discussiones Mathematicae Graph Theory

1 Dlamini G.

1 Dunbar J.

1 Frick M.

1 Oellermann O.

1 van Aardt S.

1 2005

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The directed path partition conjecture