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<p>The Turán number of a graph <i>H</i>, denoted by <i>ex</i>(<i>n, H</i>), is the maximum number of edges in any graph on <i>n</i> vertices containing no <i>H</i> as a subgraph. A linear (star) forest is a forest consisting of paths (stars). A path-star forest <i>F</i> is a forest consisting of paths and stars. In this paper, we determine <i>ex</i>(<i>n, F</i>) for sufficiently large <i>n</i> and characterize the corresponding extremal graphs, and our result generalizes previous known results on the Turán numbers of linear forests and star forests.</p>

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The Turán Number of Path-star Forests

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Xiao-na Fang,
  • Yao-jun Chen,
  • Li-hua You

摘要

The Turán number of a graph H, denoted by ex(n, H), is the maximum number of edges in any graph on n vertices containing no H as a subgraph. A linear (star) forest is a forest consisting of paths (stars). A path-star forest F is a forest consisting of paths and stars. In this paper, we determine ex(n, F) for sufficiently large n and characterize the corresponding extremal graphs, and our result generalizes previous known results on the Turán numbers of linear forests and star forests.