Hamilton Cycles in Double Generalized Petersen Graphs
Yutaro Sakamoto
TL;DR
This paper proves that all double generalized Petersen graphs contain Hamilton cycles, confirming a longstanding conjecture and expanding understanding of their Hamiltonian properties.
Contribution
The paper constructs Hamilton cycles in all double generalized Petersen graphs, establishing their Hamiltonicity and resolving a conjecture from previous research.
Findings
All DGPGs are Hamiltonian.
Constructed explicit Hamilton cycles in all DGPGs.
Confirmed the conjecture on Hamiltonicity of DGPGs.
Abstract
Watkins (1969) first introduced the generalized Petersen graphs (GPGs) by modifying Petersen graph. Zhou and Feng (2012) modified GPGs and introduced the double generalized Petersen graphs (DGPGs). Kutnar and Petecki (2016) proved that DGPGs are Hamiltonian in special cases and conjectured that all DGPGs are Hamiltonian. In this paper, we construct Hamilton cycles in all DGPGs.
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Taxonomy
Topicsgraph theory and CDMA systems · Microtubule and mitosis dynamics · Advanced Graph Theory Research