Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Symmetric Hamilton Cycle Decompositions of Complete Multigraphs

100%

Chitra V., Muthusamy A.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 4

695-707

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

Perfect Set of Euler Tours of Kp,p,p

100%

Govindan T., Muthusamy A.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 4

783-796

Bermond conjectured that if G is Hamilton cycle decomposable, then L(G), the line graph of G, is Hamilton cycle decomposable. In this paper, we construct a perfect set of Euler tours for the complete tripartite graph Kp,p,p for any prime p and hence prove Bermond’s conjecture for G = Kp,p,p.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Muthusamy A.

1 Chitra V.

1 Govindan T.

1 2016

1 2013

Wyniki wyszukiwania

Symmetric Hamilton Cycle Decompositions of Complete Multigraphs

Perfect Set of Euler Tours of Kp,p,p