| Title: | On a conjecture of Erdős on size Ramsey number of star forests |
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| Authors: | ID Davoodi, Akbar (Author)
ID Javadi, Ramin (Author)
ID Kamranian, Azam (Author)
ID Raeisi, Ghaffar (Author) |
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| Files: |  AMC_Davoodi,Javadi,Kamranian,Raeisi_2025.pdf (282,24 KB)
MD5: C287AF1EABEE18F3290CA82BBAEA5698
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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: | 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. |
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| Keywords: | size Ramsey number, star forest, Ramsey minimal graph |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.04.2025 |
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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. 25, no. 2, [article no.] P2.09 |
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| PID: | 20.500.12556/RUP-21994  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | https://doi.org/10.26493/1855-3974.3081.d6c |
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| Publication date in RUP: | 21.10.2025 |
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| Views: | 314 |
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| Downloads: | 4 |
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