Geodesic
Decomposition of the Product of Cycles Based on Degree Partition
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 1, pp. 241-256

Voir la notice de l'article provenant de la source Library of Science

The Cartesian product of n cycles is a 2n-regular, 2n-connected and bi- pancyclic graph. Let G be the Cartesian product of n even cycles and let 2n = n1+ n2+ ・ ・ ・ + nk with k ≥ 2 and ni ≥ 2 for each i. We prove that if k = 2, then G can be decomposed into two spanning subgraphs G1 and G2 such that each Gi is ni-regular, ni-connected, and bipancyclic or nearly bipancyclic. For k gt; 2, we establish that if all ni in the partition of 2n are even, then G can be decomposed into k spanning subgraphs G1, G2, . . ., Gk such that each Gi is ni-regular and ni-connected. These results are analogous to the corresponding results for hypercubes.
Keywords: hypercube, Cartesian product, n-connected, regular, bipan- cyclic, spanning subgraph 
@article{DMGT_2019_39_1_a18,
     author = {Borse, Y. M. and Shaikh, S. R.},
     title = {Decomposition of the {Product} of {Cycles} {Based} on {Degree} {Partition}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {241--256},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2019_39_1_a18/}
}
TY  - JOUR
AU  - Borse, Y. M.
AU  - Shaikh, S. R.
TI  - Decomposition of the Product of Cycles Based on Degree Partition
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2019
SP  - 241
EP  - 256
VL  - 39
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2019_39_1_a18/
LA  - en
ID  - DMGT_2019_39_1_a18
ER  - 
%0 Journal Article
%A Borse, Y. M.
%A Shaikh, S. R.
%T Decomposition of the Product of Cycles Based on Degree Partition
%J Discussiones Mathematicae. Graph Theory
%D 2019
%P 241-256
%V 39
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2019_39_1_a18/
%G en
%F DMGT_2019_39_1_a18
Borse, Y. M.; Shaikh, S. R. Decomposition of the Product of Cycles Based on Degree Partition. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 1, pp. 241-256. http://geodesic.mathdoc.fr/item/DMGT_2019_39_1_a18/