Year: 2025
Type: article
Abstract: Let T be a graph obtained by taking the Cartesian product of n cycles of even lengths ≥4. It is known that for any subset of k vertices of T with 1≤k≤2n−1, there exists a 2-factor in T where each cycle contains exactly one of the k vertices. We generalize this result to r-factors by proving that for 1≤k≤2n−r+1 and 2≤r≤2n, there exists an r-factor H in T such that each component of H is an r-regular, r-connected and bipancyclic graph, with each component containing exactly one of the k specified vertices of T. As a consequence, we obtain an analogous result for hypercubes.
Authors: A. V. Sonawane, Y. M. Borse
Institution: Savitribai Phule Pune University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,226
OpenAlex ID: W7117656183