A note on $1$-factorizability of quartic supersolvable Cayley graphs

Document Type : Research Paper

Authors

1 Department of Mathematics, Tarbiat Modares University, Tehran, Iran

2 Department of Mathematics, Tarbiat Modares University, P. O. Box 14115-137, Tehran

Abstract

Alspach et al‎. ‎conjectured that every quartic Cayley graph on an even solvable group is $1$-factorizable‎. ‎In this paper‎, ‎we verify this conjecture for quartic Cayley graphs on supersolvable groups of even order‎.

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References

[1] A. Ab dollahi, 1-factorizations of Cayley graphs, Ars Combin. , 86 (2008) 129{131.
[2] B. Alspach, Y. Liu and C. Zhang, Nowhere-zero 4-ows and Cayley graphs on solvable groups, SIAM J. Discrete
Math. , 9 (1996) 151{154.
[3] B. Alspach, M. Morton and Y. Qin, 1-factorizations of Cayley graphs on solvable groups, Rep ort, The University of Auckland Library, https://researchspace.auckland.ac.nz/bitstream/handle/2292/5039/393.pdf.
[4] R. Stong, On 1-factorizability of Cayley graphs, J. Combin. Theory Ser. B , 39 (1985) 298{307.
Transactions on Combinatorics
Volume 7, Issue 4 - Serial Number 4
December 2018
Pages 7-10

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History

  • Receive Date: 04 June 2017
  • Revise Date: 28 May 2018
  • Accept Date: 29 May 2018
  • Published Online: 01 December 2018

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