Existence of 3-regular subgraphs in Cartesian product of cycles
Let G be a graph obtained by taking the Cartesian product of finitely many cycles. It is known that G is bipancyclic, that is, G contains cycles of every even length from 4 to |V(G)|. We extend this result for the existence of 3-regular subgraphs in G. We prove that G contains a 3-regular, 2-connect...
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Taylor & Francis Group
2019-12-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0972860017301962 |
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doaj-d3ebce981f3646d79c8354397e1605ec2020-11-25T03:01:45ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002019-12-01163332342Existence of 3-regular subgraphs in Cartesian product of cyclesY.M. Borse0J.B. Saraf1Department of Mathematics, Savitribai Phule Pune University, Pune 411007, IndiaAmruteshwar College of Arts, Commerce and Science, Pune 412213, India; Corresponding author.Let G be a graph obtained by taking the Cartesian product of finitely many cycles. It is known that G is bipancyclic, that is, G contains cycles of every even length from 4 to |V(G)|. We extend this result for the existence of 3-regular subgraphs in G. We prove that G contains a 3-regular, 2-connected subgraph with l vertices if l=8 or l=12 or l is an even integer with 16≤l≤|V(G)|. For l∈{6,10,14}, we give necessary and sufficient conditions for the existence of such subgraphs in G. Keywords: Cartesian product, Hypercube, 3-connected, 3-regular, Bipancyclichttp://www.sciencedirect.com/science/article/pii/S0972860017301962 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Y.M. Borse J.B. Saraf |
| spellingShingle |
Y.M. Borse J.B. Saraf Existence of 3-regular subgraphs in Cartesian product of cycles AKCE International Journal of Graphs and Combinatorics |
| author_facet |
Y.M. Borse J.B. Saraf |
| author_sort |
Y.M. Borse |
| title |
Existence of 3-regular subgraphs in Cartesian product of cycles |
| title_short |
Existence of 3-regular subgraphs in Cartesian product of cycles |
| title_full |
Existence of 3-regular subgraphs in Cartesian product of cycles |
| title_fullStr |
Existence of 3-regular subgraphs in Cartesian product of cycles |
| title_full_unstemmed |
Existence of 3-regular subgraphs in Cartesian product of cycles |
| title_sort |
existence of 3-regular subgraphs in cartesian product of cycles |
| publisher |
Taylor & Francis Group |
| series |
AKCE International Journal of Graphs and Combinatorics |
| issn |
0972-8600 |
| publishDate |
2019-12-01 |
| description |
Let G be a graph obtained by taking the Cartesian product of finitely many cycles. It is known that G is bipancyclic, that is, G contains cycles of every even length from 4 to |V(G)|. We extend this result for the existence of 3-regular subgraphs in G. We prove that G contains a 3-regular, 2-connected subgraph with l vertices if l=8 or l=12 or l is an even integer with 16≤l≤|V(G)|. For l∈{6,10,14}, we give necessary and sufficient conditions for the existence of such subgraphs in G. Keywords: Cartesian product, Hypercube, 3-connected, 3-regular, Bipancyclic |
| url |
http://www.sciencedirect.com/science/article/pii/S0972860017301962 |
| work_keys_str_mv |
AT ymborse existenceof3regularsubgraphsincartesianproductofcycles AT jbsaraf existenceof3regularsubgraphsincartesianproductofcycles |
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