arXiv subjects

Ignacy Buczek

Publications and source records attributed to Ignacy Buczek.

2 recordsLinked to original sources

arXiv2026

Seeking the dense half in $K_4$-free graphs

We show that every $K_4$-free graph on $n$ vertices has a balanced bipartition such that neither part contains more than $0.0671n^2 + o(n^2)$ edges. This improves the previous best bound of $0.074n^2$ by Xu and Zhang. We also formulate a conjecture that the tight bound for this problem is $\frac{425}{6498}n^2 \approx 0.0654n^2$, and present a construction showing that it would be best possible.

math.CO↗

arXiv2026

Balanced bipartite distance of $K_4$-free graphs

We show that every $K_4$-free graph on $n$ vertices can be made balanced bipartite by removing at most $\frac{n^2}{9}$ edges. This proves a conjecture of Balogh, Clemen, and Lidický, and generalizes both Sudakov's result on the bipartite distance of $K_4$-free graphs and Reiher's result on the sparse half of $K_4$-free graphs.

math.CO↗