Every K_{1,d}-free graph that excludes the k-ladder as an induced minor has tree-independence number bounded by a function of k and d.
[CC16] Chandra Chekuri and Julia Chuzhoy
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Excluding a Ladder as an Induced Minor in Graphs Without Induced Stars
Every K_{1,d}-free graph that excludes the k-ladder as an induced minor has tree-independence number bounded by a function of k and d.