Computing Tree Decompositions with Small Independence Number

@article{Dallard2022ComputingTD,
  title={Computing Tree Decompositions with Small Independence Number},
  author={Cl{\'e}ment Dallard and F. Fomin and Petr A. Golovach and Tuukka Korhonen and Martin Milanivc},
  journal={ArXiv},
  year={2022},
  volume={abs/2207.09993}
}
The independence number of a tree decomposition is the maximum of the independence numbers of the subgraphs induced by its bags. The tree-independence number of a graph is the minimum independence number of a tree decomposition of it. Several NP -hard graph problems, like maximum weight independent set, can be solved in time n O ( k ) if the input graph is given with a tree decomposition of independence number at most k . However, it was an open problem if tree-independence number could be… 

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