HU, P., et al. Large Multipartite Subgraphs in H-free Graphs. In: Extended Abstracts EuroComb 2021. European Conference on Combinatorics, Graph Theory and Applications, Barcelona / online, 2021-09-06/2021-09-10. Basel: Springer Nature Switzerland AG, 2021. p. 707-713. Trends in Mathematics. vol. 14. ISSN 2297-0215. ISBN 978-3-030-83822-5. DOI 10.1007/978-3-030-83823-2_113.
In this work, we discuss a strengthening of a result of Füredi that every n-vertex K_{r+1}-free graph can be made r-partite by removing at most T(n, r) - e(G) edges, where T(n,r)=(r-1)/(2r) * n^2 denotes the number of edges of the n-vertex r-partite Turán graph. As a corollary, we answer a problem of Sudakov and prove that every K6 -free graph can be made bipartite by removing at most 4n^2/ 25 edges. The main tool we use is the flag algebra method applied to locally definied vertex-partitions.
