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- W2951623688 abstract "We study the recently introduced boolean-width of graphs. Our structural results are as follows. Firstly, we show that almost surely the boolean-width of a random graph on $n$ vertices is $O(log^2 n)$, and it is easy to find the corresponding decomposition tree. Secondly, for any constant $d$ a graph of maximum degree $d$ has boolean-width linear in treewidth. This implies that almost surely the boolean-width of a (sparse) random $d$-regular graph on $n$ vertices is linear in $n$. Thirdly, we show that the boolean-cut value is well approximated by VC dimension of corresponding set system. Since VC dimension is widely studied, we hope that this structural result will prove helpful in better understanding of boolean-width. Combining our first structural result with algorithms from Bui-Xuan et al cite{BTV09,BTV09II} we get for random graphs quasi-polynomial $O^*(2^{O(log ^4 n)})$ time algorithms for a large class of vertex subset and vertex partitioning problems." @default.
- W2951623688 created "2019-06-27" @default.
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- W2951623688 date "2009-08-19" @default.
- W2951623688 modified "2023-09-27" @default.
- W2951623688 title "On the boolean-width of a graph: structure and applications" @default.
- W2951623688 cites W1484794585 @default.
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- W2951623688 hasPublicationYear "2009" @default.
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