Year: 2026
Type: article
Abstract: We show that there exist constants delta 1 comma delta 2 greater than 0 δ 1 , δ 2 > 0 $\delta _1,\delta _2\gt 0$ such that if upper G G $G$ is an left parenthesis n comma d comma lamda right parenthesis ( n , d , λ ) $(n,d,\lambda )$ -graph with lamda divided by d less than or equals delta 1 λ / d ≤ δ 1 $\lambda /d\le \delta _1$ , then upper G G $G$ contains an induced cycle of length at least delta 2 n divided by d δ 2 n / d $\delta _2n/d$ . We further demonstrate that, up to a constant factor, this is best possible. Utilising our techniques, we derive that the number of non-isomorphic induced subgraphs of such upper G G $G$ is at least exponential in n log d divided by d n log d
Institutions: Tel Aviv University, University of Sheffield
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4416611612
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