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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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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 |
| Summary: | 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 |
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| ISSN: | 0972-8600 |