| Title: | Injective colorings of Sierpiński-like graphs and Kneser graphs |
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| Authors: | ID Brešar, Boštjan (Author)
ID Klavžar, Sandi (Author)
ID Samadi, Babak (Author)
ID Yero, Ismael G. (Author) |
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| Files: |  PDF - Presentation file, download (6,36 MB)
MD5: 8406140D4BA7AE756E30E322A1DF27C8
 URL - Source URL, visit https://link.springer.com/article/10.1007/s00373-025-02952-3
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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: | Two relationships between the injective chromatic number and, respectively, chromatic number and chromatic index, are proved. They are applied to determine the injective chromatic number of Sierpiński graphs and to give a short proof that Sierpiński graphs are Class 1. Sierpiński-like graphs are also considered, including generalized Sierpiński graphs over cycles and rooted products. It is proved that the injective chromatic number of a rooted product of two graphs lies in a set of six possible values. Sierpiński graphs and Kneser graphs $K(n,r)$ are considered with respect of being perfect injectively colorable, where a graph is perfect injectively colorable if it has an injective coloring in which every color class forms an open packing of largest cardinality. In particular, all Sierpiński graphs and Kneser graphs $K(n,r)$ with $n\ge 3r-1$, are perfect injectively colorable, while $K(7,3)$ is not. |
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| Keywords: | injective coloring, injective chromatic number, perfect injectively colorable graph, Sierpiński graphs, Kneser graphs, rooted product graph |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.08.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 22 str. |
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| Numbering: | Vol. 41, iss. 4, article no. 83 |
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| PID: | 20.500.12556/DiRROS-23099  |
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| UDC: | 519.17 |
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| ISSN on article: | 0911-0119 |
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| DOI: | 10.1007/s00373-025-02952-3 |
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| COBISS.SI-ID: | 243802627 |
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| Note: |
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| Publication date in DiRROS: | 25.07.2025 |
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| Views: | 378 |
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| Downloads: | 230 |
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| Metadata: |    |
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