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<p>For each fixed <i>d</i> ≥ 1, we obtain asymptotic estimates for the number of <i>d</i>-representable simplicial complexes on <i>n</i> vertices as a function of <i>n</i>. The case <i>d</i> = 1 corresponds to counting interval graphs, and we obtain new results in this well-studied case as well. Our results imply that the <i>d</i>-representable complexes comprise a vanishingly small fraction of <i>d</i>-collapsible complexes.</p>

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Enumeration of interval graphs and d-representable complexes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月4日

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  • Boris Bukh,
  • R. Amzi Jeffs

摘要

For each fixed d ≥ 1, we obtain asymptotic estimates for the number of d-representable simplicial complexes on n vertices as a function of n. The case d = 1 corresponds to counting interval graphs, and we obtain new results in this well-studied case as well. Our results imply that the d-representable complexes comprise a vanishingly small fraction of d-collapsible complexes.