Decomposition of Complete Graphs into Cycles and Stars

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Abstract

Let Ck denote a cycle of length k and let Sk denote a star with k edges. As usual Kn denotes the complete graph on n vertices. In this paper we investigate decomposition of Kn into Cl's and Sk's, and give some necessary or sufficient conditions for such a decomposition to exist. In particular, we give a complete solution to the problem in the case l = k = 4 as follows: For any nonnegative integers p and q and any positive integer n, there exists a decomposition of Kn into p copies of C4 and q copies of S4 if and only if 4(p + q) = q ≠ 1 if n is odd, and q ≥{3, n/2}if n is even.

Original languageEnglish
Pages (from-to)301-313
Number of pages13
JournalGraphs and Combinatorics
Volume29
Issue number2
DOIs
Publication statusPublished - 2013 Jan 1
Externally publishedYes

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Keywords

  • Complete graph
  • Cycle
  • Graph decomposition
  • Star

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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