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Extending Vertex and Edge Pancyclic Graphs

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Abstract

A graph G of order \(n\ge 3\) is pancyclic if G contains a cycle of each possible length from 3 to n, and vertex pancyclic (edge pancyclic) if every vertex (edge) is contained on a cycle of each possible length from 3 to n. A chord of a cycle is an edge between two nonadjacent vertices of the cycle, and chorded cycle is a cycle containing at least one chord. We define a graph G of order \(n\ge 4\) to be chorded pancyclic if G contains a chorded cycle of each possible length from 4 to n. In this article, we consider extensions of the property of being chorded pancyclic to chorded vertex pancyclic and chorded edge pancyclic.

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Authors and Affiliations

  1. Department of Mathematics, Cedar Crest College, Allentown, PA, 18104, USA

    Megan Cream

  2. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    Ronald J. Gould

  3. Department of Electronic and Computer Engineering, National Institute of Technology, Ibaraki College, Ibaraki, Japan

    Kazuhide Hirohata

Authors
  1. Megan Cream
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  2. Ronald J. Gould
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  3. Kazuhide Hirohata
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Correspondence to Megan Cream.

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Cream, M., Gould, R.J. & Hirohata, K. Extending Vertex and Edge Pancyclic Graphs. Graphs and Combinatorics 34, 1691–1711 (2018). https://doi.org/10.1007/s00373-018-1960-2

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  • DOI: https://doi.org/10.1007/s00373-018-1960-2

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