Symmetric Hamilton Cycle Decompositions of Complete Multigraphs
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 4, p. 695.

Voir la notice de l'article dans European Digital Mathematics Library

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
Classification : 05C45, 05C51, 05C70
Mots-clés : complete multigraph, 1-factor, symmetric Hamilton cycle, decomposition., decomposition 
@article{DMGT_2013__33_4_267866,
     author = {V. Chitra and A. Muthusamy},
     title = {Symmetric {Hamilton} {Cycle} {Decompositions} of {Complete} {Multigraphs}},
     journal = {Discussiones Mathematicae Graph Theory},
     pages = {695},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {2013},
     zbl = {1297.05138},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_4_267866/}
}
TY  - JOUR
AU  - V. Chitra
AU  - A. Muthusamy
TI  - Symmetric Hamilton Cycle Decompositions of Complete Multigraphs
JO  - Discussiones Mathematicae Graph Theory
PY  - 2013
SP  - 695
VL  - 33
IS  - 4
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_4_267866/
LA  - en
ID  - DMGT_2013__33_4_267866
ER  - 
%0 Journal Article
%A V. Chitra
%A A. Muthusamy
%T Symmetric Hamilton Cycle Decompositions of Complete Multigraphs
%J Discussiones Mathematicae Graph Theory
%D 2013
%P 695
%V 33
%N 4
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_4_267866/
%G en
%F DMGT_2013__33_4_267866
V. Chitra; A. Muthusamy. Symmetric Hamilton Cycle Decompositions of Complete Multigraphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 4, p. 695. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_4_267866/