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Nested cycles with no geometric crossings
- Publication Year :
- 2021
-
Abstract
- In 1975, Erd\H{o}s asked the following question: what is the smallest function $f(n)$ for which all graphs with $n$ vertices and $f(n)$ edges contain two edge-disjoint cycles $C_1$ and $C_2$, such that the vertex set of $C_2$ is a subset of the vertex set of $C_1$ and their cyclic orderings of the vertices respect each other? We prove the optimal linear bound $f(n)=O(n)$ using sublinear expanders.<br />Comment: 10 pages, 2 figures
- Subjects :
- Mathematics - Combinatorics
05C38, 05C35, 05C48
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2104.04810
- Document Type :
- Working Paper