On the minimal degree implying equality of the largest triangle-free and bipartite subgraphs

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Abstract

Erdo{combining double acute accent}s posed the problem of finding conditions on a graph G that imply t (G) = b (G), where t (G) is the largest number of edges in a triangle-free subgraph and b (G) is the largest number of edges in a bipartite subgraph. Let δc be the least number so that any graph G on n vertices with minimum degree δc n has t (G) = b (G). Extending results of Bondy, Shen, Thomassé and Thomassen we show that 0.75 ≤ δc < 0.791. © 2006 Elsevier Inc. All rights reserved.

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Balogh, J., Keevash, P., & Sudakov, B. (2006). On the minimal degree implying equality of the largest triangle-free and bipartite subgraphs. Journal of Combinatorial Theory. Series B, 96(6), 919–932. https://doi.org/10.1016/j.jctb.2006.03.001

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