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· 2001 · arXiv 2000.2013

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Obstructions for Minor-Closed Classes of limiting Densities Below 3/2

math.CO · 2026-06-23 · unverdicted · novelty 8.0

For every δ < 3/2 the ⊆-minimal minor-closed classes with density >δ form a finite explicitly identified set, yielding a 2^poly(n)-time algorithm that computes δ(excl(Z)) or reports ≥3/2 for any finite forbidden-minor set Z.

The density of $k$-cacti via excluding minors

math.CO · 2026-06-04 · unverdicted · novelty 7.0

k-cacti exclude large complete minors and thus have edge density O((log k / sqrt(log log k)) n), tight up to a sqrt(log log k) factor.

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  • Obstructions for Minor-Closed Classes of limiting Densities Below 3/2 math.CO · 2026-06-23 · unverdicted · none · ref 30

    For every δ < 3/2 the ⊆-minimal minor-closed classes with density >δ form a finite explicitly identified set, yielding a 2^poly(n)-time algorithm that computes δ(excl(Z)) or reports ≥3/2 for any finite forbidden-minor set Z.

  • The density of $k$-cacti via excluding minors math.CO · 2026-06-04 · unverdicted · none · ref 8

    k-cacti exclude large complete minors and thus have edge density O((log k / sqrt(log log k)) n), tight up to a sqrt(log log k) factor.