On reduced Hamilton walks

Malnič, Aleksander (avtor), Požar, Rok (avtor)

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 $n$.

• Jezik: Angleški jezik
• Ključne besede: algorithm, Hamilton walk, nonstandard metric, reduced walk
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: 11 str.
• Številčenje: Vol. 510, art. 129695
• PID: 20.500.12556/RUL-182657
• UDK: 519.17
• ISSN pri članku: 0096-3003
• DOI: 10.1016/j.amc.2025.129695
• COBISS.SI-ID: 248238083
• Datum objave v RUL: 20.05.2026

Gradivo je del revije

• Naslov: Applied mathematics and computation
• Skrajšan naslov: Appl. math. comput.
• Založnik: Elsevier
• ISSN: 0096-3003
• COBISS.SI-ID: 24983808

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: algoritem, hamiltonski sprehod, nestandardna metrika, reduciran sprehod