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Some recent results on domination in graphs

Michael D. Plummer (2006)

Discussiones Mathematicae Graph Theory

In this paper, we survey some new results in four areas of domination in graphs, namely: (1) the toughness and matching structure of graphs having domination number 3 and which are "critical" in the sense that if one adds any missing edge, the domination number falls to 2; (2) the matching structure of graphs having domination number 3 and which are "critical" in the sense that if one deletes any vertex, the domination number falls to 2; (3) upper bounds...

Some remarks on Jaeger's dual-hamiltonian conjecture

Bill Jackson, Carol A. Whitehead (1999)

Annales de l'institut Fourier

François Jaeger conjectured in 1974 that every cyclically 4-connected cubic graph G is dual hamiltonian, that is to say the vertices of G can be partitioned into two subsets such that each subset induces a tree in G . We shall make several remarks on this conjecture.

Some Remarks On The Structure Of Strong K-Transitive Digraphs

César Hernández-Cruz, Juan José Montellano-Ballesteros (2014)

Discussiones Mathematicae Graph Theory

A digraph D is k-transitive if the existence of a directed path (v0, v1, . . . , vk), of length k implies that (v0, vk) ∈ A(D). Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an acyclic transitive digraph. Also, strong 3 and 4-transitive digraphs have been characterized. In this work we analyze the structure of strong k-transitive digraphs having a cycle of length at least k. We show...

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