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A new approach to the results of Kovari, Sos, and Turan concerning rectangle-free subsets of the grid
Turan concerning rectangle-free subsets of the grid Combinatorics
2012/6/21
For positive integers $m$ and $n$, define $f(m,n)$ to be the smallest integer such that any subset $A$ of the $m \times n$ integer grid with $|A| \geq f(m,n)$ contains a rectangle; that is, there are ...
Interlacement in 4-regular graphs: a new approach using nonsymmetric matrices
4-regular graph circuit partition Euler system interlacement
2012/4/18
Let F be a 4-regular graph with an Euler system C. We introduce a simple way to modify the interlacement matrix of C so that every circuit partition P of F has an associated modified interlacement mat...