# Dwight Duffus

• 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)
• 5
• 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)
• 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)
• 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)
• 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)
• 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)
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)