| Title: | On reduced Hamilton walks |
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| Authors: | ID Malnič, Aleksander (Author)
ID Požar, Rok (Author) |
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| Files: |  PDF - Presentation file, download (1,91 MB)
MD5: FBE5B262667B45FEB56A4CE21367B6BC
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0096300325004217
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| 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. While every connected graph admits a Hamilton walk, existence of a reduced Hamilton walk is not guaranteed for all graphs. However, we prove that a reduced Hamilton walk does exist in a connected graph with minimal valency at least $2$. Furthermore, given such a graph on $n$ vertices, we present an $O(n^2)$-time algorithm that constructs a reduced Hamilton walk of length at most $n(n+3)/2$. Specifically, for a graph belonging to a family of regular expander graphs, we can find a reduced Hamilton walk of length at most $c(6n−2)\log n+2n$, where $c$ is a constant independent of $n$. |
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| Keywords: | algorithm, Hamilton walk, nonstandard metric, reduced walk |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.02.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 1-11 |
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| Numbering: | Vol. 510, art. 129695 |
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| PID: | 20.500.12556/DiRROS-23757  |
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| UDC: | 519.17 |
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| ISSN on article: | 0096-3003 |
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| DOI: | 10.1016/j.amc.2025.129695 |
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| COBISS.SI-ID: | 248238083 |
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| Publication date in DiRROS: | 01.10.2025 |
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| Views: | 175 |
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| Downloads: | 86 |
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