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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…
On the algorithmic complexity of decomposing graphs into regular/irregular structures
Arash Ahadi, Ali Dehghan, Mohammad-Reza Sadeghi +1
A locally irregular graph is a graph whose adjacent vertices have distinct degrees, a regular graph is a graph where each vertex has the same degree and a locally regular graph is…