| Title: | Variety of general position problems in graphs |
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| Authors: | ID Tian, Jing (Author)
ID Klavžar, Sandi (Author) |
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| Files: |  PDF - Presentation file, download (377,60 KB)
MD5: 6B93719702121058EF4162871595D6E9
 URL - Source URL, visit https://link.springer.com/article/10.1007/s40840-024-01788-z
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | Let $X$ be a vertex subset of a graph $G$. Then $u, v\in V(G)$ are $X$-positionable if $V(P)\cap X \subseteq \{u,v\}$ holds for any shortest $u,v$-path $P$. If each two vertices from $X$ are $X$-positionable, then $X$ is a general position set. The general position number of $G$ is the cardinality of a largest general position set of $G$ and has been already well investigated. In this paper a variety of general position problems is introduced based on which natural pairs of vertices are required to be $X$-positionable. This yields the total (resp. dual, outer) general position number. It is proved that the total general position sets coincide with sets of simplicial vertices, and that the outer general position sets coincide with sets of mutually maximally distant vertices. It is shown that a general position set is a dual general position set if and only if its complement is convex. Several sufficient conditions are presented that guarantee that a given graph has no dual general position set. The total general position number, the outer general position number, and the dual general position number of arbitrary Cartesian products are determined. |
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| Keywords: | general position, total general position, outer general position, dual general position, Cartesian product of graphs, strong resolving graph, convex subgraph |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 14 str. |
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| Numbering: | Vol. 48, iss. 1, [article no.] 5 |
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| UDC: | 519.17 |
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| ISSN on article: | 0126-6705 |
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| DOI: | 10.1007/s40840-024-01788-z  |
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| COBISS.SI-ID: | 213851395 |
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| Note: |
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| Publication date in DiRROS: | 07.11.2024 |
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| Views: | 11 |
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| Downloads: | 6 |
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| Metadata: |    |
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