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.
Tree independence number
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Verifies stronger coarse balanced separator conjecture for all r in K_{t,t}-induced-minor-free graphs of bounded clique number via a polynomial-size hitting set Z for large balls on any Y.
citing papers explorer
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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.
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Coarse Balanced Separators in Biclique-Induced-Minor-Free Graphs
Verifies stronger coarse balanced separator conjecture for all r in K_{t,t}-induced-minor-free graphs of bounded clique number via a polynomial-size hitting set Z for large balls on any Y.