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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.04726 |
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Table of Contents:
- In 1980, Gupta, Kahn and Robertson proved that every graph $G$ with minimum degree at least $k\geq 2$ contains a cycle $C$ containing at least $k+1$ vertices each having at least $k$ neighbors in $C$ (so $C$ has at least $\frac{(k+1)(k-2)}{2}$ chords). In this work, we go further by showing that some of its edges can be contracted to obtain a graph with high minimum degree (we call such a minor of $C$ a \emph{cyclic minor}). We then investigate further cycles having cliques as cyclic minors, and show that minimum degree at least $O(k^2)$ guarantees a cyclic $K_k$-minor.