Nested cycles with no geometric crossings
نویسندگان
چکیده
In 1975, Erd?s asked the following question: what is smallest function f ( n stretchy="false">) f(n) for which all graphs with alttext="n"> encoding="application/x-tex">n vertices and edges contain two edge-disjoint cycles alttext="upper C 1"> C 1 encoding="application/x-tex">C_1 2"> 2 encoding="application/x-tex">C_2 , such that vertex set of a subset their cyclic orderings respect each other? We prove optimal linear bound right-parenthesis equals upper O = O encoding="application/x-tex">f(n)=O(n) using sublinear expanders.
منابع مشابه
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2022
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/bproc/107