On the sum of the largest and smallest eigenvalues of graphs with high odd girth
Abstract
The sum of the maximum and minimum eigenvalues, and the odd girth of a graph both measure bipartiteness. We seek to relate these measures. In particular, for an odd integer , let denote the supremum of over graphs without odd cycles of length less than k . The example of the k -cycle shows that . In their recent work, Abiad, Taranchuk, and Van Veluw showed that and asked to determine the asymptotics of . Using approximation theory, we show that , giving a tight upper bound up to a poly-logarithmic factor.
Fields of Study & Subjects
Graph theory and applications
Advanced Graph Theory Research
Graph Labeling and Dimension Problems
Publication details
- Journal / source
- Linear Algebra and its Applications
- Volume
- 736
- Pages
- 1–12
- Publication date
- 26 January 2026
- Language
- EN