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- Endre SzemerÃ©di, William T. Trotter
- Combinatorica
- 1983

In this paper, we establish several theorems involving configurations of points and lines in the Euclidean plane. Our results answer questions and settle conjectures of P. Erd6s, G. Purdy, and G.â€¦ (More)

- James H. Schmerl, William T. Trotter
- Discrete Mathematics
- 1993

A hnite. indecomposabic partially ordered set is said to be critically indecomposahlc if. whenever an clement is removed. the resulting induced partially ordered set is not indccomposabic. The sameâ€¦ (More)

- LÃ¡szlÃ³ LovÃ¡sz, Michael E. Saks, William T. Trotter
- Discrete Mathematics
- 1989

One of the simplest heuristics for obtaining a proper coloring of a graph is the Fii-Fit algorithm: Fix an arbitrary ordering of the vertices and, using the positive integers as the color set, assignâ€¦ (More)

- Graham R. Brightwell, William T. Trotter
- SIAM J. Discrete Math.
- 1993

With a convex polytope M in a, a partially ordered set PM is associated whose elements are the vertices, edges, and faces of M ordered by inclusion. This paper shows that the order dimension of P Mâ€¦ (More)

- Martin Charles Golumbic, Clyde L. Monma, William T. Trotter
- Discrete Applied Mathematics
- 1984

Tolerance graphs arise from the intersection of intervals with varying tolerances in a way that generalizes both interval graphs and permutation graphs. In this paper we prove that every toleranceâ€¦ (More)

- Hal A. Kierstead, William T. Trotter
- Planar Graphs
- 1991

We show that the game chromatic number of a planar graph is at most 33. More generally, there exists a function f: f\l --+ f\l so that for each n E f\l. if a graph does not contain a homeomorph ofâ€¦ (More)

- C. ChvatÃ¡l, Vojtech RÃ¶dl, Endre SzemerÃ©di, William T. Trotter
- J. Comb. Theory, Ser. B
- 1983

The Ramsey number of a graph G is the least number t for which it is true that whenever the edges of the complete graph on t vertices are colored in an arbitrary fashion using two colors, say red andâ€¦ (More)

- Wolfgang J. Paul, Nicholas Pippenger, Endre SzemerÃ©di, William T. Trotter
- 24th Annual Symposium on Foundations of Computerâ€¦
- 1983

We show that, for multi-tape Turing machines, non-deterministic linear time is more powerful than deterministic linear time. We also discuss the prospects for extending this result to more generalâ€¦ (More)

- Peter HorÃ¡k, He Qing, William T. Trotter
- Journal of Graph Theory
- 1993

In this paper, we show that the edge set of a cubic graph can always be partitioned into 10 subsets, each of which induces a matching in the graph. This result is a special case of a generalâ€¦ (More)

- Graham R. Brightwell, William T. Trotter
- SIAM J. Discrete Math.
- 1997

This is a sequel to a previous paper entitled The Order Dimension of Convex Polytopes, by the same authors [SIAM J. Discrete Math., 6 (1993), pp. 230â€“245]. In that paper, we considered the poset PMâ€¦ (More)