Decomposition of complete tripartite graphs into cycles and paths of length three

  • Shanmugasundaram Priyadarsini Periyar University
  • Appu Muthusamy Periyar University

Abstract

Let $C_{k}$ and $P_{k}$ denote a cycle and a path on $k$ vertices, respectively. In this paper, we obtain necessary and sufficient conditions for the decomposition of $K_{{r},{s},{t}}$ into $p$ copies of $C_{3}$ and $q$ copies of $P_{4}$ for all possible values of $p$, $q\geq0$.

Author Biography

Shanmugasundaram Priyadarsini, Periyar University

Department of Mathematics

References

[1] S. Alipour, E.S. Mahmoodian, E. Mollaahmadi, On decomposing Complete
tripartite graphs into 5 -cycles, Australas. J. Combin. 54 (2012) , 289 - 301 .
[2] E.J. Billington, Decomposing complete tripartite graphs into cycles of lenght 3
and 4 , Discrete Math. 197/198 (1999) , 123 - 135 .
[3] E.J. Billington, N.J. Cavenagh, B.R. Smith, Path and Cycle decompositions
of complete equipartite graphs: 3 and 5 parts, Discrete Math. 310 (2010) ,
241 - 252 .
[4] N.J. Cavenagh, Decompositions of complete tripartite graphs into k cycles,
Australas. J. Combin. 18 (1998) , 193 - 200 .
[5] N.J. Cavenagh and E.J. Billington, On decomposing complete tripartite graphs
into 5 -cycles, Australas. J. Combin. 22 (2000) , 41 - 62 .
[6] B.R. Smith, Decomposing complete equipartite graphs into cycles of lenght 2p ,
J. Combin. Des. 16 (2008) , 244 - 252 .
[7] D. Sotteau, Decomposition of Km,n (K∗m,n ) into cycles(circuits) of lenght 2k ,
J. Combin. Theory Ser. B 30 (1981) , 75 - 81 .
Published
2020-12-22
Section
Articles