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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.11034 |
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Table of Contents:
- Let $\mathscr{F}$ be a family of graphs. A graph $G$ is $\mathscr{F}$-free if $G$ does not contain any $F\in \mathscr{F}$ as a subgraph. The Turán number, denoted by $ex(n, \mathscr{F})$, is the maximum number of edges in an $n$-vertex $\mathscr{F}$-free graph. Let $F $ be a fixed graph with $ χ(F) \geq 3 $. A forest $H$ is called a linear forest if all components of $H$ are paths. In this paper, we determined the exact value of $ex(n, \{H, F\}) $ for a fixed graph $F$ with $χ(F)\geq 3$ and a linear forest $H$ with at least $2$ components and each component with size at least $3$.