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- W3100154294 abstract "We consider one-sided error property testing of $mathcal{F}$-minor freeness in bounded-degree graphs for any finite family of graphs $mathcal{F}$ that contains a minor of $K_{2,k}$, the $k$-circus graph, or the $(ktimes 2)$-grid for any $kinmathbb{N}$. This includes, for instance, testing whether a graph is outerplanar or a cactus graph. The query complexity of our algorithm in terms of the number of vertices in the graph, $n$, is $tilde{O}(n^{2/3} / epsilon^5)$. Czumaj et~al. showed that cycle-freeness and $C_k$-minor freeness can be tested with query complexity $tilde{O}(sqrt{n})$ by using random walks, and that testing $H$-minor freeness for any $H$ that contains a cycles requires $Omega(sqrt{n})$ queries. In contrast to these results, we analyze the structure of the graph and show that either we can find a subgraph of sublinear size that includes the forbidden minor $H$, or we can find a pair of disjoint subsets of vertices whose edge-cut is large, which induces an $H$-minor." @default.
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- W3100154294 date "2017-07-19" @default.
- W3100154294 modified "2023-09-27" @default.
- W3100154294 title "A Sublinear Tester for Outerplanarity (and Other Forbidden Minors) With One-Sided Error" @default.
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