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Dichromatic number, circulant tournaments and Zykov sums of digraphs

Víctor Neumann-Lara (2000)

Discussiones Mathematicae Graph Theory

The dichromatic number dc(D) of a digraph D is the smallest number of colours needed to colour the vertices of D so that no monochromatic directed cycle is created. In this paper the problem of computing the dichromatic number of a Zykov-sum of digraphs over a digraph D is reduced to that of computing a multicovering number of an hypergraph H₁(D) associated to D in a natural way. This result allows us to construct an infinite family of pairwise non isomorphic vertex-critical k-dichromatic circulant...

Difference labelling of digraphs

Martin Sonntag (2004)

Discussiones Mathematicae Graph Theory

A digraph G is a difference digraph iff there exists an S ⊂ N⁺ such that G is isomorphic to the digraph DD(S) = (V,A), where V = S and A = {(i,j):i,j ∈ V ∧ i-j ∈ V}.For some classes of digraphs, e.g. alternating trees, oriented cycles, tournaments etc., it is known, under which conditions these digraphs are difference digraphs (cf. [5]). We generalize the so-called source-join (a construction principle to obtain a new difference digraph from two given ones (cf. [5])) and construct a difference labelling...

Digraphs contractible onto * K 3

Stefan Janaqi, François Lescure, M. Maamoun, Henry Meyniel (1998)

Mathematica Bohemica

We show that any digraph on n ≥ 3 vertices and with not less than 3 n - 3 arcs is contractible onto * K 3 .

Directed hypergraphs: a tool for researching digraphs and hypergraphs

Hortensia Galeana-Sánchez, Martín Manrique (2009)

Discussiones Mathematicae Graph Theory

In this paper we introduce the concept of directed hypergraph. It is a generalisation of the concept of digraph and is closely related with hypergraphs. The basic idea is to take a hypergraph, partition its edges non-trivially (when possible), and give a total order to such partitions. The elements of these partitions are called levels. In order to preserve the structure of the underlying hypergraph, we ask that only vertices which belong to exactly the same edges may be in the same level...

Editorial

Irina Perfilieva, Michael Wagenknecht (2009)

Acta Mathematica Universitatis Ostraviensis

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