20.500.12556/RUP-21994 On a conjecture of Erdős on size Ramsey number of star forests Domneva Erdősa o velikostnem Ramseyjevem številu zvezdnih gozdov Given two graphs F_1 and F_2, their size Ramsey number, denoted by r̂(F_1, F_2), is the minimum number of edges of a graph G such that for any edge coloring of G by colors red and blue, G contains either a red copy of F1 or a blue copy of F2. In this paper, we deal with the size Ramsey number of star forests (disjoint union of stars) and following a conjecture by Burr, Erdős, Faudree, Rousseau, and Schelp in 1978, we determine the exact value of r̂(⊔_{i = 1}^s K_{1, ni}, ⊔_{i = 1}^t K_{1, mi}) in several cases including when either m_i’s and n_i’s are odd, or s = 1 or s = 2 and n_1 = n_2. size Ramsey number star forest Ramsey minimal graph velikostno Ramseyjevo število zvezdni gozd Ramseyjev minimalni graf true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-10-21 22:43:51 2025-10-21 22:43:51 2025-11-12 03:03:32 0000-00-00 00:00:00 2025 0 0 10 str. no. 2, [article no.] P2.09 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-04-01 51 1855-3974 https://doi.org/10.26493/1855-3974.3081.d6c AMC_Davoodi,Javadi,Kamranian,Raeisi_2025.pdf AMC_Davoodi,Javadi,Kamranian,Raeisi_2025.pdf 1 C287AF1EABEE18F3290CA82BBAEA5698 83f57a698cdcbc43ad49ee95c8f5c820937da4ffe8171d1107f1849472ddf61d d790a8ba-aebf-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31929 Založba Univerze na Primorskem 0 0 0