Bill Sands

Publications (9)0.84 Total impact

• Article: On the size of maximal chains and the number of pairwise disjoint maximal antichains.

  Dwight Duffus, Bill Sands
  Discrete Mathematics. 01/2010; 310:2883-2889.
• Source

  Available from: Norbert Sauer

  Chapter: Chromatic Numbers and Homomorphisms of Large Girth Hypergraphs

  Dwight Duffus, Vojtěch Rödl, Bill Sands, Norbert Sauer
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  ABSTRACT: We consider the problem of determining the minimum chromatic number of graphs and hypergraphs of large girth which cannot be mapped under a homomorphism to a specified graph or hypergraph. More generally, we are interested in large girth hypergraphs that do not admit a vertex partition of specified size such that the subhypergraphs induced by the partition blocks have a homomorphism to a given hypergraph. In the process, a general probabilistic construction of large girth hypergraphs is obtained, and general definitions of chromatic number and homomorphisms are considered.
  12/2005: pages 455-471;
• Source

  Available from: upenn.edu

  Article: Splitting Numbers of Grids.

  Dwight Duffus, Bill Sands
  Electr. J. Comb. 01/2005; 12.
• Article: Finite distributive lattices and the splitting property

  Dwight Duffus, Bill Sands
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  ABSTRACT: We show that a finite distributive lattice has the splitting property - every maximal antichain splits into two parts so that the lattice is the union of the upset of one part and the downset of the other - if and only if it is a Boolean lattice or is one of three other lattices. We also introduce a measure of "how splitting" a finite distributive lattice is, and investigate it.
  Algebra Universalis 03/2003; 49(1):13-33. · 0.43 Impact Factor
• Article: An inequality for the sizes of prime filters of finite distributive lattices.

  Dwight Duffus, Bill Sands
  Discrete Mathematics. 01/1999; 201:89-99.
• Article: Two-colouring all two-element maximal antichains.

  Dwight Duffus, Bill Sands, Norbert Sauer, Robert E. Woodrow
  J. Comb. Theory, Ser. A. 01/1991; 57:109-116.
• Article: Maximal Chains and Antichains in Boolean Lattices.

  Dwight Duffus, Bill Sands, Peter Winkler
  SIAM J. Discrete Math. 01/1990; 3:197-205.
• Article: Lexicographic matchings cannot form Hamiltonian cycles

  Dwight Duffus, Bill Sands, Robert Woodrow
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  ABSTRACT: For any positive integer k let B(k) denote the bipartite graph of k- and k+1-element subsets of a 2k+1-element set with adjacency given by containment. It has been conjectured that for all k, B(k) is Hamiltonian. Any Hamiltonian cycle would be the union of two (perfect) matchings. Here it is shown that for all k>1 no Hamiltonian cycle in B(k) is the union of two lexicographic matchings.
  Order 05/1988; 5(2):149-161. · 0.41 Impact Factor
• Article: On monochromatic paths in edge-coloured digraphs.

  Bill Sands, Norbert Sauer, Robert E. Woodrow
  J. Comb. Theory, Ser. B. 01/1982; 33:271-275.