# Max Cuts in Triangle-Free Graphs

@inproceedings{Balogh2021MaxCI, title={Max Cuts in Triangle-Free Graphs}, author={J{\'o}zsef Balogh and Felix Christian Clemen and Bernard Lidick'y}, year={2021} }

A well-known conjecture by Erdős states that every trianglefree graph on n vertices can be made bipartite by removing at most n/25 edges. This conjecture was known for graphs with edge density at least 0.4 and edge density at most 0.172. Here, we will extend the edge density for which this conjecture is true; we prove the conjecture for graphs with edge density at most 0.2486 and for graphs with edge density at least 0.3197. Further, we prove that every triangle-free graph can be made bipartite…

## 4 Citations

### More about sparse halves in triangle-free graphs

- Mathematics
- 2022

One of Erdős’s conjectures states that every triangle-free graph on vertices has an induced subgraph on vertices with at most edges. We report several partial results towards this conjecture. In…

### 10 Problems for Partitions of Triangle-free Graphs

- Mathematics
- 2022

We will state 10 problems, and solve some of them, for partitions in triangle-free graphs related to Erd˝os’ Sparse Half Conjecture. Among others we prove the following variant of it: For every…

### The Spectrum of Triangle-free Graphs

- Mathematics
- 2022

Denote by q n ( G ) the smallest eigenvalue of the signless Laplacian matrix of an n -vertex graph G . Brandt conjectured in 1997 that for regular triangle-free graphs q n ( G ) ≤ 4 n 25 . We prove a…

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