On reduced Hamilton walksMalnič, Aleksander (Avtor) Požar, Rok (Avtor) algorithmHamilton walknonstandard metricreduced walkA 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 $n$.20262026-05-20 11:18:39Članek v reviji182657sl