| Title: | On (r,g,χ)- graphs and cages of regularity r, girth g and chromatic number χ |
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| Authors: | ID Araujo-Pardo, Gabriela (Author)
ID Díaz-Calderón, Julio César (Author)
ID Fresán-Figueroa, Julián (Author)
ID González-Moreno, Diego (Author)
ID Lesniak, Linda (Author)
ID Olsen, Mika (Author) |
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| Files: |  ADAM_Araujo-Pardo,Diaz-Calderón,Fresan-Figueroa,Gonzalez-Moreno,Lesniak,Olsen_2025.pdf (408,46 KB)
MD5: B44DB9981933796858D24BC328361B9B
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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: | ZUP - University of Primorska Press
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| Abstract: | For integers r ≥ 2, g ≥ 3 and χ ≥ 2, an (r, g, χ)-graph is an r-regular graph with girth g and chromatic number χ. Such a graph of minimum order is called an (r, g, χ)-cage. Here we prove the existence of (r, g, χ)-graphs for all r and even g when χ = 2 and for all r and g when χ = 3. Furthermore, using both existence proofs and explicit constructions we give examples of (r, g, χ)-graphs for infinitely many values of r, g, χ. |
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| Keywords: | graphs, cages, girth, chromatic number |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 11.06.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 10 str. |
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| Numbering: | Vol. 8, no. 3, [article no.] P3.07 |
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| PID: | 20.500.12556/RUP-22079  |
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| UDC: | 519.17 |
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| eISSN: | 2590-9770 |
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| DOI: | 10.26493/2590-9770.1737.0f8 |
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| Publication date in RUP: | 03.11.2025 |
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| Views: | 183 |
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| Downloads: | 2 |
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