June 18, 2024Open Access

Tree independence number III. Thetas, prisms and stars

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Tree independence number is bounded by a constant tau in every graph excluding thetas, prisms, and complete bipartite stars K1,t as induced subgraphs.
Theoretical proof demonstrates that for any positive integer t, forbidding theta subgraphs, prisms, and K1,t stars guarantees tree independence number bounds.
Structural bound holds even when prisms contain a path of length zero, revealing structural sparsity properties across theta-free and prism-free graphs.

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Implication

Theoretical analysis proves bounded tree independence number in theta-, prism-, and star-free graphs, indicating structural limits on independent sets.

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Chudnovsky et al. (2024) studied this question.

synapsesocial.com/papers/68e643efb6db6435875d5c7f https://doi.org/10.48550/arxiv.2406.13053

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Implication

Theoretical analysis proves bounded tree independence number in theta-, prism-, and star-free graphs, indicating structural limits on independent sets.

Tree independence number III. Thetas, prisms and stars

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Implication

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Tree independence number III. Thetas, prisms and stars

Key Points

Discussion

Implication

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