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- Michael Dorfling, Michael A. Henning
- Discrete Applied Mathematics
- 2006

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex covering and dominating set problems inâ€¦ (More)

- Michael Dorfling, Wayne Goddard, Michael A. Henning
- Ars Comb.
- 2006

MacGillivray and Seyffarth (J. Graph Theory 22 (1996), 213â€“229) proved that planar graphs of diameter three have domination number at most ten. Recently it was shown (J. Graph Theory 40 (2002), 1â€“25)â€¦ (More)

- Izak Broere, Michael Dorfling, Jean E. Dunbar, Marietjie Frick
- Discussiones Mathematicae Graph Theory
- 1998

Let Ï„(G) denote the number of vertices in a longest path of the graph G and let k1 and k2 be positive integers such that Ï„(G) = k1+k2. The question at hand is whether the vertex set V (G) can beâ€¦ (More)

- Michael Dorfling, Samantha Dorfling
- Discussiones Mathematicae Graph Theory
- 2002

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let P and Q be hereditary properties of graphs. The generalizedâ€¦ (More)

- Michael Dorfling, Michael A. Henning
- Eur. J. Comb.
- 2014

For k â‰¥ 2, let H be a k-uniform hypergraph on n vertices and m edges. The transversal number Ï„(H) of H is the minimum number of vertices that intersect every edge. ChvÃ¡tal andMcDiarmid [V. ChvÃ¡tal,â€¦ (More)

- Peter Dankelmann, Michael Dorfling
- Discrete Mathematics
- 2016

In this paper we consider upper bounds on the diameter of Eulerian digraphs containing a vertex of large degree. Define the maximum degree of a digraph to be the maximum of all in-degrees andâ€¦ (More)

- Izak Broere, Michael Dorfling
- Discussiones Mathematicae Graph Theory
- 2000

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If P1, . . . ,Pn are properties of graphs, then a (P1, . . .â€¦ (More)

- Michael Dorfling, Samantha Dorfling
- Discussiones Mathematicae Graph Theory
- 2012

For a graph G and a vertex-coloring c : V (G) â†’ {1, 2, . . . , k}, the color code of a vertex v is the (k + 1)-tuple (a0, a1, . . . , ak), where a0 = c(v), and for 1 â‰¤ i â‰¤ k, ai is the number ofâ€¦ (More)

- Michael Dorfling, Johannes H. Hattingh, Elizabeth Jonck
- Discrete Applied Mathematics
- 2017

We show that the total domination number of a maximal outerplanar graph G is bounded above by n+k 3 , where n is the order of G and k is the number of vertices of degree 2. For k > n 3 , a betterâ€¦ (More)

- Michael Dorfling, Johan Meyer
- The American Mathematical Monthly
- 2012