| Naslov: | Span of a graph : keeping the safety distance |
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| Avtorji: | ID Banič, Iztok (Avtor)
ID Taranenko, Andrej (Avtor) |
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| Datoteke: |  RAZ_Banic_Iztok_2023.pdf (213,47 KB)
MD5: 1AA92015C783649B7951098931849AE4
 https://doi.org/10.46298/dmtcs.9859
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Članek v reviji |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | FNM - Fakulteta za naravoslovje in matematiko
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| Opis: | Inspired by Lelek's idea from [Disjoint mappings and the span of spaces, Fund. Math. 55 (1964), 199 -- 214], we introduce the novel notion of the span of graphs. Using this, we solve the problem of determining the \emph{maximal safety distance} two players can keep at all times while traversing a graph. Moreover, their moves must be made with respect to certain move rules. For this purpose, we introduce different variants of a span of a given connected graph. All the variants model the maximum safety distance kept by two players in a graph traversal, where the players may only move with accordance to a specific set of rules, and their goal: visit either all vertices, or all edges. For each variant, we show that the solution can be obtained by considering only connected subgraphs of a graph product and the projections to the factors. We characterise graphs in which it is impossible to keep a positive safety distance at all moments in time. Finally, we present a polynomial time algorithm that determines the chosen span variant of a given graph. |
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| Ključne besede: | strong span of a graph, direct span of a graph, Cartesian span of a graph, safety distance |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Poslano v recenzijo: | 29.07.2022 |
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| Datum sprejetja članka: | 19.02.2023 |
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| Datum objave: | 01.03.2023 |
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| Založnik: | Association DMTCS |
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| Leto izida: | 2023 |
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| Št. strani: | 19 str. |
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| Številčenje: | Vol. 25, no. 1 |
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| PID: | 20.500.12556/DKUM-88137  |
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| UDK: | 519.17 |
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| COBISS.SI-ID: | 148408835 |
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| DOI: | 10.46298/dmtcs.9859 |
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| ISSN pri članku: | 1365-8050 |
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| Datum objave v DKUM: | 07.06.2024 |
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| Število ogledov: | 228 |
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| Število prenosov: | 32 |
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| Metapodatki: |    |
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| Področja: | Ostalo
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