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This is a Quantitative Study study.

September 30, 2025Open Access

Tree-width of a graph excluding an apex-forest or a wheel as a minor

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Proves that f(H) equals |V(H)|-1 for every apex-forest H, demonstrating a tighter bound.
Shows f(H) is bounded above by max{(3/2)|V(H)|-9/2, |V(H)|-1} for wheels, expanding known limits.
Research focuses on planar graphs without disjoint cycles, improving understanding of minor relationships.
Findings refine previous work by Leaf and Seymour, addressing properties of large graphs achieving the lower bound.

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This paper reveals bounds on tree-width for planar graphs, indicating apex-forests yield simpler structures.

Liu et al. (2025) studied this question.

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