#### Filter Results:

- Full text PDF available (8)

#### Publication Year

1972

2017

- This year (0)
- Last 5 years (6)
- Last 10 years (9)

#### Publication Type

#### Co-author

#### Journals and Conferences

Learn More

- Jean E. Dunbar, Jerrold W. Grossman, Johannes H. Hattingh, Stephen T. Hedetniemi, Alice A. McRae
- Discrete Mathematics
- 1997

Let G = (V,E) be a connected undirected graph. For any vertex v âˆˆ V , the closed neighborhood of v is N [v] = {v} âˆª {u âˆˆ V | uv âˆˆ E }. For S âŠ† V , the closed neighborhood of S is N [S] = â‹ƒ vâˆˆS N [v].â€¦ (More)

- Jean E. Dunbar, David J. Erwin, Teresa W. Haynes, Sandra Mitchell Hedetniemi, Stephen T. Hedetniemi
- Discrete Applied Mathematics
- 2006

We say that a function f : V â†’ {0, 1, . . . , diam(G)} is a broadcast if for every vertex v âˆˆ V , f(v) â‰¤ e(v), where diam(G) denotes the diameter of G and e(v) denotes the eccentricity of v. The costâ€¦ (More)

- Jean E. Dunbar, Stephen T. Hedetniemi, Michael A. Henning, Alice A. McRae
- Discrete Mathematics
- 1999

We introduce one of many classes of problems which can be defined in terms of 3-valued functions on the vertices of a graph G = (V, E) of the form f : V + { 1, 0, l}. Such a fknction is said to be aâ€¦ (More)

- Susan A. van Aardt, Alewyn P. Burger, Jean E. Dunbar, Marietjie Frick, John Harris, Joy Singleton
- Electr. J. Comb.
- 2013

A digraph is k-traceable if its order is at least k and each of its subdigraphs of order k is traceable. The Traceability Conjecture (TC) states that for k > 2 every k-traceable oriented graph ofâ€¦ (More)

- Jean E. Dunbar, Frederick C. Harris, Sandra Mitchell Hedetniemi, Stephen T. Hedetniemi, Alice A. McRae, Renu C. Laskar
- Discrete Mathematics
- 1995

In a graph G = (V; E), a set of vertices S is nearly perfect if every vertex in V ? S is adjacent to at most one vertex in S. Nearly perfect sets are closely related to 2-packings of graphs, stronglyâ€¦ (More)

- Gayla S. Domke, Jean E. Dunbar, Lisa R. Markus
- Discrete Mathematics
- 1997

Let 7(G) denote the minimum cardinality of a dominating set of a graph G = (V,E). A longstanding upper bound for 7(G) is attributed to Berge: For any graph G with n vertices and maximum degree A(G),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)

- Marietjie Frick, Susan A. van Aardt, Gcina Dlamini, Jean E. Dunbar, Ortrud R. Oellermann
- Discussiones Mathematicae Graph Theory
- 2005

The Directed Path Partition Conjecture is the following: If D is a digraph that contains no path with more than Î» vertices then, for every pair (a, b) of positive integers with Î» = a + b, thereâ€¦ (More)

- Jean E. Dunbar, Marietjie Frick
- Discrete Mathematics
- 2007

The detour order of a graph G, denoted by (G), is the order of a longest path in G. The Path Partition Conjecture (PPC) is the following: If G is any graph and (a, b) any pair of positive integersâ€¦ (More)

- Jean E. Dunbar, Marietjie Frick, Frank Bullock
- Discrete Mathematics
- 2004