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Progress on the traceability conjecture for oriented graphs

Abstract : A digraph is k-traceable if each of its induced subdigraphs of order k is traceable. The Traceability Conjecture is that for k ≥ 2 every k-traceable oriented graph of order at least 2k − 1 is traceable. The conjecture has been proved for k ≤ 5. We prove that it also holds for k = 6.
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Marietjie Frick, Peter Katrenič. Progress on the traceability conjecture for oriented graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2008, Vol. 10 no. 3 (3), pp.105--113. ⟨10.46298/dmtcs.428⟩. ⟨hal-00972339⟩

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