MWIS on ordered graphs excluding a single induced ordered subgraph H is classified into polynomial, quasipolynomial, subexponential, or NP-hard for every H.
Subexponential-time algorithms for maximum independent set inP t-free and broom-free graphs.Algorithmica, 81(2):421–438
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Maximum Weight Independent Set in Hereditary Classes of Ordered Graphs
MWIS on ordered graphs excluding a single induced ordered subgraph H is classified into polynomial, quasipolynomial, subexponential, or NP-hard for every H.