Results and Problems on Chorded Cycles: A Survey

被引：1
|
作者：
Gould, Ronald J. [1 ]
机构：
[1] Emory Univ, Dept Math, Atlanta, GA 30322 USA
来源：
GRAPHS AND COMBINATORICS | 2022年 / 38卷 / 06期
关键词：
Chord; Cycle; Chorded cycle; Pancyclic; VERTEX-DISJOINT CYCLES; LONGEST CIRCUITS; NEIGHBORHOOD UNIONS; INDEPENDENT CYCLES; GRAPHS; NUMBER; CONJECTURE; EXISTENCE;
D O I：
10.1007/s00373-022-02586-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A chord of a cycle C is an edge between two non-consecutive vertices of the cycle. A cycle C in a graph G is chorded if the vertex set of C induces at least one chord. In 1961 Posa formulated a natural question: What conditions imply a graph contains a chorded cycle? In this paper, we survey results and problems that relate to Posa's question on chorded cycles in graphs. These include sufficient conditions for a chorded cycle to exist, or sets of chorded cycles exist, or cycles with multiple chords exist, or chorded cycles with additional properties exist.
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页数：27
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