14
votes
Accepted
Finding subgraphs with high treewidth and constant degree
See the paper by Julia Chuzhoy and myself on Treewidth sparsifiers.
We show that one can obtain a subgraph of degree at most 3 with treewidth $\Omega(k/polylog(k))$ where $k$ is the treewidth of $G$. ...
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11
votes
Random functions of low degree as a real polynomial
Here's an algorithm that beats the trivial attempts.
The following is a known fact (Exercise 1.12 in O'Donnell's book) : If $f:\{-1,1\}^n\to\{-1,1\}$ is a Boolean function which has degree $\le d$ as ...
- 353
1
vote
Finding subgraphs with high treewidth and constant degree
In the case of pathwidth, reposting here a comment made to me by email by Benjamin Rossman back in 2020 (see also the comments to the answer https://cstheory.stackexchange.com/a/38943):
Every graph G ...
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