On the Turan number of forests
Bernard Lidick\'y, Hong Liu, Cory Palmer

TL;DR
This paper determines the maximum number of edges in large graphs that avoid certain forest subgraphs, specifically paths and stars, and characterizes the extremal graphs for these cases.
Contribution
It generalizes previous results by explicitly finding Turan numbers and extremal graphs for forests of paths and stars, extending known bounds.
Findings
Exact Turan numbers for forests of paths and stars
Unique extremal graphs identified for large n
Generalization of previous results by Bushaw and Kettle
Abstract
The Turan number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not have H as a subgraph. We determine the Turan number and find the unique extremal graph for forests consisting of paths when n is sufficiently large. This generalizes a result of Bushaw and Kettle [ Combinatorics, Probability and Computing 20:837--853, 2011]. We also determine the Turan number and extremal graphs for forests consisting of stars of arbitrary order.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
