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Dimensional edge fault-tolerant Hamiltonicity of (folded) hypercubes.

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Title: Dimensional edge fault-tolerant Hamiltonicity of (folded) hypercubes.
Authors: Cai, Junqing1,2 (AUTHOR), Chen, Meirun3 (AUTHOR), Lin, Cheng-Kuan1,4 (AUTHOR) cklin@nycu.edu.tw
Source: Discrete Applied Mathematics. May2026, Vol. 384, p154-164. 11p.
Subjects: Hypercubes, Fault tolerance (Engineering), Parallel programming, Hamiltonian graph theory
Abstract: The hypercube Q n and folded hypercube F Q n serve as fundamental interconnection network topologies in parallel computing, valued for their efficient communication and inherent fault tolerance. This paper investigates their resilience to dimensional-edge faults with respect to three critical Hamiltonian properties: Hamiltonicity, Hamiltonian laceability, and hyper Hamiltonian laceability. We establish precise bounds for fault tolerance in these structures, proving that: (1) For Q n , both the dimensional-edge fault-tolerant Hamiltonicity and Hamiltonian laceability equal 2 n − 1 − n , while hyper Hamiltonian laceability tolerates up to 2 n − 1 − 2 n + 2 ; (2) For F Q n , the dimensional-edge fault-tolerant Hamiltonicity is 2 n − n ; (3) For odd-dimensional F Q 2 n + 1 , the dimensional-edge fault-tolerant Hamiltonian laceability and hyper Hamiltonian laceability are 2 2 n + 1 − 2 n − 1 and 2 2 n + 1 − 4 n , respectively. These results significantly advance our understanding of fault tolerance in cube-based network topologies and provide rigorous theoretical guarantees for their reliable operation in practical systems. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:The hypercube Q n and folded hypercube F Q n serve as fundamental interconnection network topologies in parallel computing, valued for their efficient communication and inherent fault tolerance. This paper investigates their resilience to dimensional-edge faults with respect to three critical Hamiltonian properties: Hamiltonicity, Hamiltonian laceability, and hyper Hamiltonian laceability. We establish precise bounds for fault tolerance in these structures, proving that: (1) For Q n , both the dimensional-edge fault-tolerant Hamiltonicity and Hamiltonian laceability equal 2 n − 1 − n , while hyper Hamiltonian laceability tolerates up to 2 n − 1 − 2 n + 2 ; (2) For F Q n , the dimensional-edge fault-tolerant Hamiltonicity is 2 n − n ; (3) For odd-dimensional F Q 2 n + 1 , the dimensional-edge fault-tolerant Hamiltonian laceability and hyper Hamiltonian laceability are 2 2 n + 1 − 2 n − 1 and 2 2 n + 1 − 4 n , respectively. These results significantly advance our understanding of fault tolerance in cube-based network topologies and provide rigorous theoretical guarantees for their reliable operation in practical systems. [ABSTRACT FROM AUTHOR]
ISSN:0166218X
DOI:10.1016/j.dam.2025.12.051