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<p>A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. We find an asymptotics for the number of labeled connected series-parallel tetracyclic graphs with a large number of vertices. We prove that under a uniform probability distribution, the probability of the fact that a labeled connected tetracyclic graph is a series-parallel graph is asymptotically equal to 141<i>/</i>221.</p>

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Asymptotical Enumeration of Labeled Series-Parallel Tetracyclic Graphs

  • 期刊论文

  • 发表日期：

    2025年2月26日

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  • V. A. Voblyi

摘要

A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. We find an asymptotics for the number of labeled connected series-parallel tetracyclic graphs with a large number of vertices. We prove that under a uniform probability distribution, the probability of the fact that a labeled connected tetracyclic graph is a series-parallel graph is asymptotically equal to 141/221.