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.
Induced subgraphs and tree decompositions XIX
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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2026 3representative citing papers
An edge-colored complete graph that avoids a monochromatic induced complete join can be partitioned into boundedly many simple pieces, in any number of overlapping colors.
The class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, paw, or diamond.
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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Forcing monochromatic induced subgraphs
An edge-colored complete graph that avoids a monochromatic induced complete join can be partitioned into boundedly many simple pieces, in any number of overlapping colors.
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Clique-width and induced topological minors
The class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, paw, or diamond.