ON THE ERD\H{O}S-GYÁRFÁS CONJECTURE FOR SOME CAYLEY GRAPHS

Authors

  • M. Ghasemi Department of Mathematics, Khoy Branch, Islamic Azad University, Khoy 58168-44799, Iran Author
  • R. Varmazyar Department of Mathematics, Khoy Branch, Islamic Azad University, Khoy 58168-44799, Iran Author

Keywords:

Erd\H{o}s-Gyárf\'s conjecture, Cayley graphs, cycles of graphs

Subjects:

05C38, 20B25

Abstract

In 1995, Paul Erd\H{o}s and András Gyárfás conjectured thatfor every graph $X$ of minimum degree at least $3$, there exists a non-negative integer $m$ such that $X$ contains a simple cycle of length $2^m$.In this paper, we prove that the conjecture holds for Cayley graphs of order $2p^2$ and $4p$.

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Published

2021-01-15

Issue

Vol. 73 No. 1 (2021): Vol. 73, Issue 1

Section

Articles

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This work is licensed under a Creative Commons Attribution 4.0 International License.