20.500.12556/RUL-182657 On reduced Hamilton walks 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 $n$. algorithm Hamilton walk nonstandard metric reduced walk algoritem hamiltonski sprehod nestandardna metrika reduciran sprehod true false true Angleški jezik Slovenski jezik Članek v reviji 2026-05-20 11:18:39 2026-05-20 11:18:41 2026-05-21 04:57:13 0000-00-00 00:00:00 2026 0 0 11 str. art. 129695 Vol. 510 1 Feb. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 0096-3003 10.1016/j.amc.2025.129695 248238083 1-s2.0-S0096300325004217-main.pdf 1-s2.0-S0096300325004217-main.pdf 1 BFFD13ABFBCA67711FD3C78B8375DFE3 768b223c01249f31a3375f6e981bb85124abc179d77f0fad0dfab7056747722d 57172e9a-542e-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=234116 https://www.sciencedirect.com/science/article/pii/S0096300325004217 1 93c69340-542c-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=234115 Pedagoška fakulteta 0 0 0