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Results and Problems on Chorded Cycles: A Survey

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Abstract

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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Acknowledgements

The author acknowledges the research facilities provided by Emory University.

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The author is supported by the Heilbrun Distinguished Emeritus Fellowship from Emory University.

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  1. Department of Mathematics, Emory University, Atlanta, GA, 30322, USA

    Ronald J. Gould

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Gould, R.J. Results and Problems on Chorded Cycles: A Survey. Graphs and Combinatorics 38, 189 (2022). https://doi.org/10.1007/s00373-022-02586-9

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