Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.19888 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- After long-term efforts, the Hamilton path (cycle) problem for connected vertex-transitive graphs of order $pq$ (where $p$ and $q$ are primes) was finally resolved in 2021, see [10]. Fifteen years ago, mathematicians began addressing this problem for graphs of order $2pq$. Among these studies, it was proved in 2012 (see [21]) that every connected vertex-transitive graph of order $10p$ (where $p \neq 7$ is a prime) contains a Hamilton path, with the exception of a family of graphs that was recently confirmed in [11]. In this paper, we achieve a further result: every connected vertex-transitive graph of order $10p$ (where $p$ is a prime) contains a Hamilton cycle, except for the truncation of the Petersen graph.