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44 papers · 1 filter
Orthogonal Latin Squares of Order Ten with Two Relations: A SAT Investigation
Curtis Bright, Amadou Keita, Brett Stevens
A -net() is a combinatorial design equivalent to mutually orthogonal Latin squares of order . A relation in a net is a linear dependency over in the i…
Myrvold's Results on Orthogonal Triples of Latin Squares: A SAT Investigation
Curtis Bright, Amadou Keita, Brett Stevens
Ever since E. T. Parker constructed an orthogonal pair of Latin squares in 1959, an orthogonal triple of Latin squares has been one of the most sought-aft…
Tight bound for the Erdős-Pósa property of tree minors
Vida Dujmović, Gwenaël Joret, Piotr Micek +1
Let be a tree on vertices. We prove that for every positive integer and every graph , either contains pairwise vertex-disjoint subgraphs each having a mi…
The grid-minor theorem revisited
Vida Dujmović, Robert Hickingbotham, Jędrzej Hodor +6
We prove that for every planar graph of treedepth , there exists a positive integer such that for every -minor-free graph , there exists a graph of treewidth a…
The Excluded Tree Minor Theorem Revisited
Vida Dujmović, Robert Hickingbotham, Gwenaël Joret +3
We prove that for every tree of radius , there is an integer such that every -minor-free graph is contained in for some graph with pathwidth at m…
Rank-based linkage I: triplet comparisons and oriented simplicial complexes
R. W. R. Darling, Will Grilliette, Adam Logan
Rank-based linkage is a new tool for summarizing a collection of objects according to their relationships. These objects are not mapped to vectors, and ``similarity'' between o…