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- Kenneth P. Bogart, Garth Isaak
- Discrete Mathematics
- 1998

We say any order ~ is a tolerance order on a set of vertices if we may assign to each vertex x an interval Ix of real numbers and a real number tx called a tolerance in such a way that x~,y if andâ€¦ (More)

- Garth Isaak
- Graphs and Combinatorics
- 2004

A graph is f -choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. We characterize f -choosable functions for block graphsâ€¦ (More)

- Kenneth P. Bogart, Peter C. Fishburn, Garth Isaak, Larry J. Langley
- Discrete Applied Mathematics
- 1995

We answer a question of Golumbic, Monma and Trotter by constructing proper tolerance graphs that are not unit tolerance graphs. An infinite family of graphs that are minimal in this respect isâ€¦ (More)

- Garth Isaak
- Eur. J. Comb.
- 2006

The digraphs P (n, k) have vertices corresponding to length k permutations of an n set and arcs corresponding to (k + 1) permutations. Answering a question of Starling, Klerlein, Kier and Carr weâ€¦ (More)

An (R, S; m, n)k-de Bruijn torus is a k-ary R Ã— S toroidal array with the property that every k-ary m Ã— n matrix appears exactly once contiguously on the torus. The torus is a generalization of deâ€¦ (More)

- Michael J. Fisher, Garth Isaak
- Discrete Mathematics
- 2008

We determine the values of s and t for which there is a coloring of the edges of the complete bipartite graph Ks,t which admits only the identity automorphism. In particular this allows us toâ€¦ (More)

- David E. Brown, Arthur H. Busch, Garth Isaak
- Discrete Mathematics & Theoretical Computerâ€¦
- 2010

- Jonelle Hook, Garth Isaak
- Discrete Applied Mathematics
- 2011

The graph Ramsey number R(G, H) is the smallest integer r such that every 2-coloring of the edges of Kr contains either a red copy of G or a blue copy of H . We find the largest star that can beâ€¦ (More)

High sensitivity Doppier spectroscopy of integral sunlight in the 769.9 nm line of neutral potassium reveals several equally spaced lines of Q > 1,000 centred on the well known period of 5 min. Theseâ€¦ (More)

- Garth Isaak
- 2007

Our goal in this paper is to illustrate how the representation theorems for finite interval orders and semiorders can be seen as special instances of existence results for potentials in digraphs.â€¦ (More)