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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 ...
Bondage number of grid graphs
Domination bondage number Cartesian product graph strong product graphs direct product graphs
2012/4/18
The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $...
Grid Representations and the Chromatic Number
Grid Representations the Chromatic Number Combinatorics
2012/4/17
A grid drawing of a graph maps vertices to grid points and edges to line segments that avoid grid points representing other vertices. We show that there is a number of grid points that some line segme...