| Naslov: | On reduced Hamilton walks |
|---|
| Avtorji: | ID Malnič, Aleksander (Avtor)
ID Požar, Rok (Avtor) |
|---|
| Datoteke: |  PDF - Predstavitvena datoteka, prenos (1,91 MB)
MD5: FBE5B262667B45FEB56A4CE21367B6BC
 URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0096300325004217
|
|---|
| Jezik: | Angleški jezik |
|---|
| Tipologija: | 1.01 - Izvirni znanstveni članek |
|---|
| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
|
|---|
| Povzetek: | 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 $n$. |
|---|
| Ključne besede: | algorithm, Hamilton walk, nonstandard metric, reduced walk |
|---|
| Status publikacije: | Objavljeno |
|---|
| Verzija publikacije: | Objavljena publikacija |
|---|
| Datum objave: | 01.02.2026 |
|---|
| Leto izida: | 2026 |
|---|
| Št. strani: | str. 1-11 |
|---|
| Številčenje: | Vol. 510, art. 129695 |
|---|
| PID: | 20.500.12556/DiRROS-23757  |
|---|
| UDK: | 519.17 |
|---|
| ISSN pri članku: | 0096-3003 |
|---|
| DOI: | 10.1016/j.amc.2025.129695 |
|---|
| COBISS.SI-ID: | 248238083 |
|---|
| Datum objave v DiRROS: | 01.10.2025 |
|---|
| Število ogledov: | 170 |
|---|
| Število prenosov: | 81 |
|---|
| Metapodatki: |    |
|---|
|
:
|
Kopiraj citat |
|---|
| | | | Objavi na: |  |
|---|
Postavite miškin kazalec na naslov za izpis povzetka. Klik na naslov izpiše
podrobnosti ali sproži prenos. |
