Polynomial-time algorithms exist for all CMSO2-expressible sparse induced subgraph problems in P7-free graphs of bounded clique number.
Quasi-polynomial-time algorithm for independent set in Pt-free graphs via shrinking the space of induced paths
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Sparse induced subgraphs in $P_7$-free graphs of bounded clique number
Polynomial-time algorithms exist for all CMSO2-expressible sparse induced subgraph problems in P7-free graphs of bounded clique number.