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On the Circumference of 3-Connected Cubic Triangle-Free Plane Graphs

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  • Adthasit Sinna
  • Witthawas Phanthawimol
  • Sirirat Singhun
  • M. M. Bhatti

Abstract

The circumference of a graph G is the length of a longest cycle in G, denoted by cirG. For any even number n, let cn  = min {cirG|G is a 3-connected cubic triangle-free plane graph with n vertices}. In this paper, we show that an upper bound of cn is n+1−3⌊n/136⌋ for n≥136.

Suggested Citation

  • Adthasit Sinna & Witthawas Phanthawimol & Sirirat Singhun & M. M. Bhatti, 2021. "On the Circumference of 3-Connected Cubic Triangle-Free Plane Graphs," Journal of Mathematics, Hindawi, vol. 2021, pages 1-6, August.
    • Handle: RePEc:hin:jjmath:1593006
    DOI: 10.1155/2021/1593006
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