20.500.12556/RUP-22079 On (r,g,χ)- graphs and cages of regularity r, girth g and chromatic number χ (r,g,χ)-grafi in kletke regularnosti r, ožineg in s kromatskim številom χ 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. graphs cages girth chromatic number grafi kletke ožina kromatsko število true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-11-03 12:46:40 2025-11-03 12:46:40 2025-11-18 03:05:57 0000-00-00 00:00:00 2025 0 0 10 str. no. 3, [article no.] P3.07 Vol. 8 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-06-11 519.17 2590-9770 10.26493/2590-9770.1737.0f8 ADAM_Araujo-Pardo,Diaz-Calderón,Fresan-Figueroa,Gonzalez-Moreno,Lesniak,Olsen_2025.pdf ADAM_Araujo-Pardo,Diaz-Calderón,Fresan-Figueroa,Gonzalez-Moreno,Lesniak,Olsen_2025.pdf 1 B44DB9981933796858D24BC328361B9B c32fb74bf580858f7da25e7e2016be52515dec796cee69c79683d51b62e7b2e7 a5b1f1d2-b8ab-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32024 Založba Univerze na Primorskem 0 0 0