Symmetric Hamilton Cycle Decompositions of Complete Multigraphs

• Autorzy: V. Chitra , A. Muthusamy
• Języki publikacji: EN

Abstrakty

EN

Let n ≥ 3 and ⋋ ≥ 1 be integers. Let ⋋Kn denote the complete multigraph with edge-multiplicity ⋋. In this paper, we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m for all even ⋋ ≥ 2 and m ≥ 2. Also we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m − F for all odd ⋋ ≥ 3 and m ≥ 2. In fact, our results together with the earlier results (by Walecki and Brualdi and Schroeder) completely settle the existence of symmetric Hamilton cycle decomposition of ⋋Kn (respectively, ⋋Kn − F, where F is a 1-factor of ⋋Kn) which exist if and only if ⋋(n − 1) is even (respectively, ⋋(n − 1) is odd), except the non-existence cases n ≡ 0 or 6 (mod 8) when ⋋ = 1

Słowa kluczowe

EN

complete multigraph; 1-factor; symmetric Hamilton cycle; decomposition.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 4
• Strony: 695-707

Daty

wydano

2013-09-01

online

2013-10-15

Twórcy

autor

V. Chitra

• Department of Mathematics Periyar University Salem-636 011, TN, India

autor

A. Muthusamy

• Department of Mathematics Periyar University Salem-636 011, TN, India

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1687