Exact extremizers for ℓ_p-judicious bisections of triangle-free graphs

@misc{wu2026exact,
  title = {{Exact extremizers for $\ell_p$-judicious bisections of triangle-free graphs}},
  author = {Shufei Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25902},
  eprint = {2610.25902},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25902},
}

TY  - UNPB
TI  - Exact extremizers for ℓ_p-judicious bisections of triangle-free graphs
AU  - Shufei Wu
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25902
UR  - https://arxiv.org/abs/2610.25902
AB  - Balogh, Clemen and Lidický asked how large the minimum ℓ_p-norm of the internal-edge counts over balanced partitions of an n-vertex triangle-free graph can be. For each fixed 2<p<∞ and all sufficiently large even n, we determine this value exactly for bisections and characterize all extremal graphs. They are precisely the complete bipartite graphs K_a,n−a for which a≤ n/2 maximizes an explicit integer objective. All maximizing values of a lie in an interval of length bounded in terms of p alone. We also prove quantitative stability for the same range of p and n: for sufficiently small δ≥ 0, every n-vertex triangle-free graph with bisection value at least the asymptotic optimum minus δn^2 is within O_p(δn^2+n) edge edits of a complete bipartite graph with the optimal limiting class ratio.
ER  -