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- W2005644434 abstract "Linear rank-width is a graph width parameter, which is a variation of rank-width by restricting its tree to a caterpillar. As a corollary of known theorems, for each k, there is a finite set mathcal{O}_k of graphs such that a graph G has linear rank-width at most k if and only if no vertex-minor of G is isomorphic to a graph in mathcal{O}_k. However, no attempts have been made to bound the number of graphs in mathcal{O}_k for k >= 2. We construct, for each k, 2^{Omega(3^k)} pairwise locally non-equivalent graphs that are excluded vertex-minors for graphs of linear rank-width at most k. Therefore the number of graphs in mathcal{O}_k is at least double exponential." @default.
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- W2005644434 date "2013-02-28" @default.
- W2005644434 modified "2023-09-23" @default.
- W2005644434 title "Excluded vertex-minors for graphs of linear rank-width at most k." @default.
- W2005644434 doi "https://doi.org/10.4230/lipics.stacs.2013.221" @default.
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