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On a conjecture of quintas and arc-traceability in upset tournaments

100%

Busch A., Jacobson M., Reid K.

Discussiones Mathematicae Graph Theory

2005

tom 25

nr 3

225-239

A digraph D = (V,A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V, i.e., hamiltonian path. We prove a conjecture of Quintas [7]: if D is arc-traceable, then the condensation of D is a directed path. We show that the converse of this conjecture is false by providing an example of an upset tournament which is not arc-traceable. We then give a characterization for upset tournaments in terms of their score sequences, characterize which arcs of an upset tournament lie on a hamiltonian path, and deduce a characterization of arc-traceable upset tournaments.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Busch A.

1 Jacobson M.

1 Reid K.

1 2005

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On a conjecture of quintas and arc-traceability in upset tournaments