Off-diagonal book Ramsey numbers
نویسندگان
چکیده
Abstract The book graph $B_n ^{(k)}$ consists of $n$ copies $K_{k+1}$ joined along a common $K_k$ . In the prequel to this paper, we studied diagonal Ramsey number $r(B_n ^{(k)}, B_n ^{(k)})$ Here consider natural off-diagonal variant $r(B_{cn} B_n^{(k)})$ for fixed $c \in (0,1]$ more general setting, show that an interesting dichotomy emerges: very small $c$ , simple $k$ -partite construction dictates function and all nearly-extremal colourings are close being -partite, while, bounded away from $0$ random appropriate density asymptotically optimal quasirandom. Our investigations also open up range questions about what happens intermediate values
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ژورنال
عنوان ژورنال: Combinatorics, Probability & Computing
سال: 2023
ISSN: ['0963-5483', '1469-2163']
DOI: https://doi.org/10.1017/s0963548322000360