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Algebraically Grid-Like Graphs have Large Tree-Width

2019
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Electronic Journal of Combinatorics
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By the Grid Minor Theorem of Robertson and Seymour, every graph of sufficiently large tree-width contains a large grid as a minor. Tree-width may therefore be regarded as a measure of 'grid-likeness' of a graph. The grid contains a long cycle on the perimeter, which is the $\mathbb{F}_2$-sum of the rectangles inside. Moreover, the grid distorts the metric of the cycle only by a factor of two. We prove that every graph that resembles the grid in this algebraic sense has large tree-width: Let $k,

doi:10.37236/7691
fatcat:eve2vwzxqrh2nj4tdq4zxvgmqq