| Title: | Span of a graph : keeping the safety distance |
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| Authors: | ID Banič, Iztok (Author)
ID Taranenko, Andrej (Author) |
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| Files: |  RAZ_Banic_Iztok_2023.pdf (213,47 KB)
MD5: 1AA92015C783649B7951098931849AE4
 https://doi.org/10.46298/dmtcs.9859
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | 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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| Keywords: | strong span of a graph, direct span of a graph, Cartesian span of a graph, safety distance |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 29.07.2022 |
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| Article acceptance date: | 19.02.2023 |
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| Publication date: | 01.03.2023 |
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| Publisher: | Association DMTCS |
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| Year of publishing: | 2023 |
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| Number of pages: | 19 str. |
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| Numbering: | Vol. 25, no. 1 |
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| PID: | 20.500.12556/DKUM-88137  |
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| UDC: | 519.17 |
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| ISSN on article: | 1365-8050 |
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| COBISS.SI-ID: | 148408835 |
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| DOI: | 10.46298/dmtcs.9859 |
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| Publication date in DKUM: | 07.06.2024 |
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| Views: | 225 |
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| Downloads: | 32 |
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| Metadata: |    |
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| Categories: | Misc.
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