Bipancyclic properties of faulty hypercubes
type: Item
instance of: scholarly article
title: Bipancyclic properties of faulty hypercubes
zbMATH Open document ID: 1257.68115
DOI: 10.5402/2012/308595
author: Chun-Nan Hung
author: Min-Kun Hsiao
published in: ISRN Discrete Mathematics
publication date: 2013-02-21T00:00:00Z
review text: Summary: A bipartite graph \(G = (V, E)\) is bipancyclic if it contains cycles of every even length from 4 to \(|V|\) and edge bipancyclic if every edge lies on a cycle of every even length from 4 to \(|V|\). Let \(Q_n\) denote the \(n\)-dimensional hypercube. Let \(F\) be a subset of \(V(Q_n) \cup E(Q_n)\) such that \(F\) can be decomposed into two parts \(F_{av}\) and \(F_e\), where \(F_{av}\) is a union of \(f_{av}\) disjoint adjacent pairs of \(V(Q_n)\), and \(F_e\) consists of \(f_e\) edges. We prove that \(Q_n - F\) is bipancyclic if \(f_{av} + f_e \leq n - 2\). Moreover, \(Q_n - F\) is edge bipancyclic if \(f_{av} + f_e \leq n - 2\) with \(f_{av} < n - 2\).
Mathematics Subject Classification ID: 68R10
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 68M10
zbMATH DE Number: 6137695
Wikidata QID: Q58690764
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/308595
OpenAlex ID: W2135361529
cites work: Q4230379
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description: scientific article; zbMATH DE number 6137695