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- Dwight Duffus, Bill Sands, Robert E. Woodrow
- Journal of Graph Theory
- 1985

This paper concerns an intriguing conjecture involving vertex colorings of products of graphs. First we specify the product. Given (irreflexive, symmetric) graphs G and H, the product G x H has vertex set V(G) X V ( H ) and edges all pairs {(g, h), (g‘, h’)} such that gg‘ and hh’ are edges of G and H, respectively. We avoid modifying the label “product,” in… (More)

- Dwight Duffus, Bill Sands, Peter Winkler
- SIAM J. Discrete Math.
- 1990

The following equivalent results in the Boolean lattice 2 are proven. (a) Every fibre of 2 contains a maximal chain. (b) Every cutset of 2 contains a maximal antichain. (c) Every red-blue colouring of the vertices of 2 produces either a red maximal chain or a blue maximal antichain. (d) Given any n antichains in 2 there is a disjoint maximal antichain.… (More)

- Dwight Duffus, Norbert Sauer
- Discrete Mathematics
- 1996

We discuss Hedetniemi's conjecture in the context of categories of relational structures under homomorphisms. In this language Hedetniemi's conjecture says that if there are no homomorphisms from the graphs G and H to the complete graph on n vertices then there is no homomorphism from G x H to the complete graph. If an object in some category has just this… (More)

- Dwight Duffus, Mark Ginn, Vojtech Rödl
- Random Struct. Algorithms
- 1995

Let (G, <) be a finite graph G with a linearly ordered vertex set V. We consider the decision problem (G, <)ORD to have as an instance an (unordered) graph r and as a question whether there exists a linear order < on V(T) and an order preserving graph isomorphism of (G, <) onto an induced subgraph of r. Several familiar classes of graph are characterized as… (More)

- Dwight Duffus, Bill Sands, Norbert Sauer, Robert E. Woodrow
- J. Comb. Theory, Ser. A
- 1991

- Dwight Duffus, Hanno Lefmann, Vojtech Rödl
- Discrete Mathematics
- 1995

- Dwight Duffus, Hal A. Kierstead, William T. Trotter
- J. Comb. Theory, Ser. A
- 1991

A Jbre F of a partially ordered set P is a subset which intersects each nontrivial maximal antichain of P. Let I be the smallest constant such that each finite partially ordered set P contains a fibre of size at most I ‘1 PI. We show that 1, < 3 by finding a good 3-coloring of the nontrivial antichains of P. Some decision problems involving iibres are also… (More)

- Dwight Duffus, Bill Sands
- Discrete Mathematics
- 1999

Let L be a finite distributive lattice, and let J(L) denote the set of all join-irreducible elements of L. Set j (L) = IJ(Z)l. For each a C J(L), let u(a) denote the number of elements in the prime filter {x C L: x >~a}. Our main theorem is Theorem 1. For any finite distributive lattice L, 4 "(a) ~>j(L)41q ,'2. aEJ(L) The base 4 here can most likely be… (More)

- Martin Aigner, Dwight Duffus, Daniel J. Kleitman
- Discrete Mathematics
- 1991

Denote by G and D, respectively, the the homomorphism poset of the finite undirected and directed graphs, respectively. A maximal antichain A in a poset P splits if A has a partition (B, C) such that for each p ∈ P either b ≤P p for some b ∈ B or p ≤p c for some c ∈ C. We construct both splitting and non-splitting infinite maximal antichains in G and in D.… (More)