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12 papers · 1 filter
A SAT-based Resolution of Lam's Problem
Curtis Bright, Kevin K. H. Cheung, Brett Stevens +2
In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam's problem from projective geometry$\unicode{x2014}$the long-standing problem of determining if a p…
A class of graphs with large rankwidth
Chính Hoàng, Nicolas Trotignon
We describe several graphs with arbitrarily large rankwidth (or equivalently with arbitrarily large cliquewidth). Korpelainen, Lozin, and Mayhill [Split permutation graphs, Graphs…
Nonexistence Certificates for Ovals in a Projective Plane of Order Ten
Curtis Bright, Kevin K. H. Cheung, Brett Stevens +2
In 1983, a computer search was performed for ovals in a projective plane of order ten. The search was exhaustive and negative, implying that such ovals do not exist. However, no no…
Unsatisfiability Proofs for Weight 16 Codewords in Lam's Problem
Curtis Bright, Kevin K. H. Cheung, Brett Stevens +2
In the 1970s and 1980s, searches performed by L. Carter, C. Lam, L. Thiel, and S. Swiercz showed that projective planes of order ten with weight 16 codewords do not exist. These se…
A Nonexistence Certificate for Projective Planes of Order Ten with Weight 15 Codewords
Curtis Bright, Kevin Cheung, Brett Stevens +3
Using techniques from the fields of symbolic computation and satisfiability checking we verify one of the cases used in the landmark result that projective planes of order ten do n…
Solving the clique cover problem on (bull, )-free graphs
Kathie Cameron, Chính T. Hoàng
We give an algorithm to find a minimum clique cover of a (bull, )-free graph, or equivalently, a minimum colouring of a (bull, )-free graph, where is the nu…