### Abstract

Let P _{k+1} denote a path of length k and let C _{k} denote a cycle of length k. A triangle is a cycle of length three. As usual K _{n} denotes the complete graph on n vertices. It is shown that for all nonnegative integers p and q and for all positive integers n, K _{n} can be decomposed into p copies of P _{4} and q copies of C _{3} if and only if 3(p + q) = e(K _{n}), p ‡1 if n is odd, and p ≥ n/2 1/2 n is even.

Original language | English |
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Pages (from-to) | 209-224 |

Number of pages | 16 |

Journal | Ars Combinatoria |

Volume | 107 |

Publication status | Published - 2012 Oct 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Shyu, T. W. (2012). Decomposition of complete graphs into paths of length three and triangles.

*Ars Combinatoria*,*107*, 209-224.