Hereditary classes defined by finitely many excluded induced subgraphs have bounded tree-α iff they are (tw,ω)-bounded, i.e., exclude K_{a,a}, forests with components of at most three leaves, and their line graphs.
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Tree-alpha and excluding finitely many graphs
Hereditary classes defined by finitely many excluded induced subgraphs have bounded tree-α iff they are (tw,ω)-bounded, i.e., exclude K_{a,a}, forests with components of at most three leaves, and their line graphs.