Abstract
Let \({\cal F} = \{ {H_1}, \ldots ,{H_k}\} \,\,(k \ge 1)\) be a family of graphs. The Turán number of the family \({\cal F}\) is the maximum number of edges in an n-vertex {H1, …, Hk}-free graph, denoted by ex(n, \({\cal F}\)) or ex(n, {H1,H2, … Hk}). The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different. In this paper we determine the Turán number of the family consisting of a blow-up of a cycle and a blow-up of a star in terms of the Turán number of the family consisting of a cycle, a star and linear forests with k edges.
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Acknowledgements We would like to appreciate the useful suggestions of the reviewers.
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Supported by the National Nature Science Foundation of China (Grant Nos. 11871329, 11971298)
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Wu, Z.W., Kang, L.Y. Turán Number of the Family Consisting of a Blow-up of a Cycle and a Blow-up of a Star. Acta. Math. Sin.-English Ser. 39, 1980–1988 (2023). https://doi.org/10.1007/s10114-023-1297-5
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DOI: https://doi.org/10.1007/s10114-023-1297-5