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International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 153-163 | Cite as

On Decomposing the Complete Graph into the Union of Two Disjoint Cycles

  • Saad I. El-Zanati
  • Uthoomporn Jongthawonwuth
  • Heather Jordon
  • Charles Vanden Eynden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)

Abstract

Let G of order n be the vertex-disjoint union of an even and an odd cycle. It is known that there exists a G-decomposition of \(K_v\) for all \(v \equiv 1 \pmod {2n}\). We use an extension of the Bose construction for Steiner triple systems and a recent result on the Oberwolfach Problem for 2-regular graphs with two components to show that there exists a G-decomposition of \(K_{v}\) for all \(v \equiv n \pmod {2n}\), unless \(G = C_4\cup C_5\) and \(v = 9\).

Keywords

Graph decomposition Bose construction Disjoint cycles 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Saad I. El-Zanati
    • 1
  • Uthoomporn Jongthawonwuth
    • 2
  • Heather Jordon
    • 1
  • Charles Vanden Eynden
    • 1
  1. 1.Illinois State UniversityNormalUSA
  2. 2.Chulalongkorn UniversityBangkokThailand

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