English

The Tur\'an number of path-star forests

Combinatorics 2024-12-11 v4

Abstract

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

Keywords

Cite

@article{arxiv.2305.11680,
  title  = {The Tur\'an number of path-star forests},
  author = {Xiaona Fang and Yaojun Chen and Lihua You},
  journal= {arXiv preprint arXiv:2305.11680},
  year   = {2024}
}