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Covering a Strong Digraph by α−1 Disjoint Paths: A Proof of Las Vergnas' Conjecture. Stéphan Thomassé. Laboratoire LaPCS, UFR de Mathématiques, ...
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1) irt a strong digraph such that both indegree and outdegree of each internal ... A nontrivial minimal strong digraph has at least one reducible chain. ...
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Corollary 2.2 Every strong digraph D with (D) > 1 has an ((D) - 1)-path partition. Remark 1 The case (D) = 1 of Theorem 2 is Camion's Theorem [4]: every strong tournament has a directed hamiltonian cycle. I gratefully thank J.A. Bondy for helpful discussions during the preparation of this paper.
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Comm.), we prove that every strong digraph has a spanning strong subgraph with at most n + 2α - 2 arcs, where α is the size of a maximum stable set of D. Such a spanning subgraph can be found in polynomial time.
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Stéphane Bessy , Stéphan Thomassé, Every strong digraph has a spanning strong subgraph with at most n+2α-2 arcs, Journal of Combinatorial Theory Series B, v.87 n.2, p.289-299, March 2003...
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Every strong digraph with stability α is spanned by the union of α circuits. .... Let D be a strong digraph with a coherent cyclic order C. The ...
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Let D be a strong digraph, and let V (D), E(D) and dD denote the vertex set of D, the edge set of D and the (directed) distance function of D, respectively. ...
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CiteSeerX - Document Details (Isaac Councill, Lee Giles): Answering a question of Adrian Bondy [4], we prove that every strong digraph has a spanning strong subgraph with at most n + 2α - 2 arcs, where α is the size of a maximum stable set of D. Such a spanning subgraph... ... 2 Spanning a strong digraph by cycles,
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S. Thomass e, Covering a strong digraph by 1 disjoint paths, a proof of Las Vergnas' conjecture, J. Combin. Theory Ser. B, 83 (2001), 331-333. ... Every Strong Digraph has a Spanning Strong Subgraph with.. - Bessy, Thomassé Self-citation (Thomass) (Correct)
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Creates a digraph where the vertices are the strongly connected components of Digraph as returned by strong_components/1. ... Only vertices that are included in some cycle in Digraph are returned, otherwise the returned list is equal to that returned by strong_components/1.
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