East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t) INTO GREGARIOUS m-CYCLES

  • Kim, Seong Kun (School of General Studies, Kangwon National University)
  • Received : 2013.05.15
  • Accepted : 2013.06.04
  • Published : 2013.06.01
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Abstract

For an even integer m at least 4 and any positive integer $t$, it is shown that the complete equipartite graph $K_{km(2t)}$ can be decomposed into edge-disjoint gregarious m-cycles for any positive integer ${\kappa}$ under the condition satisfying ${\frac{{(m-1)}^2+3}{4m}}$ < ${\kappa}$. Here it will be called a gregarious cycle if the cycle has at most one vertex from each partite set.

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References

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