{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T08:04:19Z","timestamp":1648713859017},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","funder":[{"name":"Department of Science and Technology, SERB, Government of India","award":["SR\/S4\/MS: 750\/12"],"award-info":[{"award-number":["SR\/S4\/MS: 750\/12"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,6]]},"abstract":"<jats:p> We consider the problem of determining the possible orders for [Formula: see text]-regular, [Formula: see text]-connected and bipancyclic subgraphs of the hypercube [Formula: see text] For [Formula: see text] and [Formula: see text] the solution to the problem is known. In this paper, we solve the problem for [Formula: see text] by proving that [Formula: see text] has a 4-regular, 4-connected and bipancyclic subgraph on [Formula: see text] vertices if and only if [Formula: see text] or [Formula: see text] is an even integer such that [Formula: see text] Further, by improving a result of Ramras, we prove that a [Formula: see text]-regular subgraph of [Formula: see text] is either isomorphic to [Formula: see text] or has at least [Formula: see text] vertices. We also improve a result of Mane and Waphare regarding the existence of a [Formula: see text]-regular, [Formula: see text]-connected and bipancyclic subgraph of [Formula: see text] Some applications of our results are given. <\/jats:p>","DOI":"10.1142\/s179383091750032x","type":"journal-article","created":{"date-parts":[[2017,3,20]],"date-time":"2017-03-20T23:07:45Z","timestamp":1490051265000},"page":"1750032","source":"Crossref","is-referenced-by-count":5,"title":["On 4-regular 4-connected bipancyclic subgraphs of hypercubes"],"prefix":"10.1142","volume":"09","author":[{"given":"Y. M.","family":"Borse","sequence":"first","affiliation":[{"name":"Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India"}]},{"given":"S. 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