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On reduced Hamilton walks

Author

Listed:
  • Malnič, Aleksander
  • Požar, Rok

Abstract

A Hamilton walk in a finite graph is a walk, either open or closed, that traverses every vertex at least once. Here, we introduce Hamilton walks that are reduced in the sense that they avoid immediate backtracking: a reduced Hamilton walk never traverses the same edge forth and back consecutively.

Suggested Citation

  • Malnič, Aleksander & Požar, Rok, 2026. "On reduced Hamilton walks," Applied Mathematics and Computation, Elsevier, vol. 510(C).
    • Handle: RePEc:eee:apmaco:v:510:y:2026:i:c:s0096300325004217
    DOI: 10.1016/j.amc.2025.129695
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    References listed on IDEAS

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    1. Yang, Hong & Liu, Juan & Meng, Jixiang, 2024. "Antidirected spanning closed trail in tournaments," Applied Mathematics and Computation, Elsevier, vol. 462(C).
    2. Gerard J. Chang & Ting-Pang Chang & Li-Da Tong, 2012. "Hamiltonian numbers of Möbius double loop networks," Journal of Combinatorial Optimization, Springer, vol. 23(4), pages 462-470, May.
    3. Li-Da Tong & Hao-Yu Yang, 2017. "Hamiltonian numbers in oriented graphs," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1210-1217, November.
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