# Search results for: Susan van Aardt

Discussiones Mathematicae Graph Theory > 2013 > 33 > 2 > 261-275

Discrete Mathematics > 2009 > 309 > 22 > 6415-6424

Discussiones Mathematicae Graph Theory > 2005 > 25 > 3 > 331-343

Discussiones Mathematicae Graph Theory > 2013 > 33 > 2 > 261-275

In 1982 Laborde, Payan and Xuong [Independent sets and longest directed paths in digraphs, in: Graphs and other combinatorial topics (Prague, 1982) 173-177 (Teubner-Texte Math., 59 1983)] conjectured that every digraph has an independent detour transversal (IDT), i.e. an independent set which intersects every longest path. Havet [Stable set meeting every longest path, Discrete Math. 289 (2004) 169-173]...

Discrete Mathematics > 2009 > 309 > 22 > 6415-6424

If every vertex of a graph is an endvertex of a hamiltonian path, then the graph is called homogeneously traceable. If we require each vertex of a graph to be an endvertex of a longest path (not necessarily a hamiltonian path), then we call the graph a detour homogeneous graph. The concept of a homogeneously traceable graph was extended to digraphs by Bermond, Simões-Pereira, and C.M. Zamfirescu....

Discussiones Mathematicae Graph Theory > 2005 > 25 > 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...