2-Subcoloring and Two Sets Cut-Uncut on fat-object intersection graphs in d dimensions admit 2^{O~(n^{1-1/(d+1)})} algorithms with ETH-tight lower bounds, via a new win-win theorem on sublinear separators leaving components with sublinear independence number.
The parameterized complexity landscape of two-sets cut-uncut.arXiv preprint arXiv:2408.13543
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Small Independent Sets versus Small Separator in Geometric Intersection Graphs
2-Subcoloring and Two Sets Cut-Uncut on fat-object intersection graphs in d dimensions admit 2^{O~(n^{1-1/(d+1)})} algorithms with ETH-tight lower bounds, via a new win-win theorem on sublinear separators leaving components with sublinear independence number.