| Title: | On general position sets in Cartesian products |
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| Authors: | ID Klavžar, Sandi (Author)
ID Patkós, Balázs (Author)
ID Rus, Gregor (Author)
ID Yero, Ismael G. (Author) |
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| Files: |  Klavzar-2021-On_General_Position_Sets_in_Carte.pdf (586,20 KB)
MD5: C14A2A5ADF9631A8E0549ABC09E7D481
 https://doi.org/10.1007/s00025-021-01438-x
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
FOV - Faculty of Organizational Sciences in Kranj
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| Abstract: | The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three distinct vertices from S lie on a common geodesic; such sets are refereed to as gp-sets of G. The general position number of cylinders Pr ◻ Cs is deduced. It is proved that (Cr ◻ Cs)∈{6,7} whenever r ≥ s ≥ 3, s ≠ 4, and r ≥ 6. A probabilistic lower bound on the general position number of Cartesian graph powers is achieved. Along the way a formula for the number of gp-sets in Pr ◻ Ps, where r,s ≥ 2, is also determined. |
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| Keywords: | general position problem, Cartesian product of graphs, paths and cycles, probabilistic constructions, exact enumeration |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 04.11.2020 |
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| Article acceptance date: | 17.05.2021 |
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| Publication date: | 26.05.2021 |
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| Publisher: | Birkhäuser |
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| Year of publishing: | 2021 |
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| Number of pages: | Str. 1-21 |
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| Numbering: | Letn. 76, Št. 3, št. članka 123 |
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| PID: | 20.500.12556/DKUM-90235  |
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| UDC: | 519.17 |
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| ISSN on article: | 1422-6383 |
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| COBISS.SI-ID: | 64926723 |
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| DOI: | 10.1007/s00025-021-01438-x |
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| Publication date in DKUM: | 27.08.2024 |
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| Views: | 224 |
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| Downloads: | 10 |
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| Metadata: |    |
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| Categories: | Misc.
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