Nested cycles with no geometric crossings-Reference-Cited by-同舟云学术

Nested cycles with no geometric crossings

Published:2022-02-07 Issue:3 Volume:9 Page:22-32
ISSN:2330-1511
Container-title:Proceedings of the American Mathematical Society, Series B
language:en
Short-container-title:Proc. Amer. Math. Soc. Ser. B

Author:

Fernández Irene,Kim Jaehoon,Kim Younjin,Liu Hong

Abstract

In 1975, Erdős asked the following question: what is the smallest function f ( n ) f(n) for which all graphs with n n vertices and f ( n ) f(n) edges contain two edge-disjoint cycles C 1 C_1 and C 2 C_2 , such that the vertex set of C 2 C_2 is a subset of the vertex set of C 1 C_1 and their cyclic orderings of the vertices respect each other? We prove the optimal linear bound f ( n ) = O ( n ) f(n)=O(n) using sublinear expanders.

Funder

Engineering and Physical Sciences Research Council

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology,Discrete Mathematics and Combinatorics,Analysis,Algebra and Number Theory

Link

https://www.ams.org/bproc/2022-09-03/S2330-1511-2022-00107-X/S2330-1511-2022-00107-X.pdf

Reference16 articles.

1. Nested cycles in graphs;Bollobás, Béla,1978

2. Proof of a conjecture of Bollobás on nested cycles;Chen, Guantao;J. Combin. Theory Ser. B,1996

3. On the maximal number of independent circuits in a graph;Corradi, K.;Acta Math. Acad. Sci. Hungar.,1963

4. Vertex-disjoint cycles of the same length;Egawa, Yoshimi;J. Combin. Theory Ser. B,1996

5. Problems and results in graph theory and combinatorial analysis;Erdős, P.,1976

Cited by 11 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Sublinear Expanders and Their Applications;Surveys in Combinatorics 2024;2024-06-13

2. Separating path systems of almost linear size;Transactions of the American Mathematical Society;2024-06-11

3. The Extremal Number of Cycles with All Diagonals;International Mathematics Research Notices;2024-04-18

4. Towards the Erdős-Gallai cycle decomposition conjecture;Advances in Mathematics;2024-02

5. Cycles with many chords;Random Structures & Algorithms;2024-01-10