Bibliographic Details
| Title: |
The minimum edge-pancyclic graph of a given order |
| Authors: |
Zhao, Xiamiao, Yang, Yuxuan, Lu, Mei |
| Publication Year: |
2025 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Combinatorics |
| More Details: |
A graph $G$ of order $n$ is called edge-pancyclic if, for every integer $k$ with $3 \leq k \leq n$, every edge of $G$ lies in a cycle of length $k$. Determining the minimum size $f(n)$ of a simple edge-pancyclic graph with $n$ vertices seems difficult. Recently, Li, Liu and Zhan \cite{li2024minimum} gave both a lower bound and an upper bound of $f(n)$. In this paper, we improve their lower bound by considering a new class of graphs and improve the upper bound by constructing a family of edge-pancyclic graphs. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2503.05506 |
| Accession Number: |
edsarx.2503.05506 |
| Database: |
arXiv |
