Document Type
Lecture
Publication Date
10-25-2023
Abstract
A graph G is H-saturated if G contains no copy of the graph H, but for any missing edge e of G, there exists a copy of H in G + e. The saturation number of the graph H, denoted by sat(n,H), is the minimal number of edges among all H-saturated graphs with n vertices. A star on a + 1 vertices and a edges is a graph by joining one vertex (called center) to all other a vertices. In this talk, we focus on the saturation number sat(n,St+1,t+1), where St+1,t+1 is called a balanced double star obtained by adding an edge between the centers of two stars St+1. We firstly prove the new upper bound sat(n,St+1,t+1) ≤ tn 2 + t+1 2 andestablish the graph achieving this upper bound. Specifically, we will determine the saturation number for St,t for sufficiently large n and small t. Finally, we will also provide the upper bounds for unbalanced double stars Sa+1,b+1 where a < b. This is joint work with Dr. Bing Wei.
Relational Format
presentation
Recommended Citation
Zhong, Lei, "Saturation Numbers of Double Stars" (2023). Combinatorics Seminar. 15.
https://egrove.olemiss.edu/math_combinatorics/15
