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Opis: 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(n2)-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)logn+2n, where c is a constant independent of n.
Ključne besede: algorithm, Hamilton walk, nonstandard metric, reduced walk
Objavljeno v RUP: 09.09.2025; Ogledov: 525; Prenosov: 7
Celotno besedilo (1,91 MB)
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