Displaying similar documents to “A proper subclass of MacLane's class 𝒜 .”

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

Arthur H. Busch, Michael S. Jacobson, K. Brooks Reid (2005)

Discussiones Mathematicae Graph Theory

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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...

Multiple routing strategies in a labelled network

J. Maublanc, D. Peyrton, A. Quilliot (2001)

RAIRO - Operations Research - Recherche Opérationnelle

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We present here models and algorithms for the construction of efficient path systems, robust to possible variations of the characteristics of the network. We propose some interpretations of these models and proceed to numerical experimentations of the related algorithms. We conclude with a discussion of the way those concepts may be applied to the design of a Public Transportation System.

On monochromatic paths and bicolored subdigraphs in arc-colored tournaments

Pietra Delgado-Escalante, Hortensia Galeana-Sánchez (2011)

Discussiones Mathematicae Graph Theory

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Consider an arc-colored digraph. A set of vertices N is a kernel by monochromatic paths if all pairs of distinct vertices of N have no monochromatic directed path between them and if for every vertex v not in N there exists n ∈ N such that there is a monochromatic directed path from v to n. In this paper we prove different sufficient conditions which imply that an arc-colored tournament has a kernel by monochromatic paths. Our conditions concerns to some subdigraphs of T and its quasimonochromatic...

The arc-width of a graph.

Barát, János, Hajnal, Péter (2001)

The Electronic Journal of Combinatorics [electronic only]

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Decompositions of a complete multidigraph into almost arbitrary paths

Mariusz Meszka, Zdzisław Skupień (2012)

Discussiones Mathematicae Graph Theory

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For n ≥ 4, the complete n-vertex multidigraph with arc multiplicity λ is proved to have a decomposition into directed paths of arbitrarily prescribed lengths ≤ n - 1 and different from n - 2, unless n = 5, λ = 1, and all lengths are to be n - 1 = 4. For λ = 1, a more general decomposition exists; namely, up to five paths of length n - 2 can also be prescribed.