Author

Binlong Li

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Review Oct 2026

Proof of the mad conjecture and its coloring applications

For a finite graph $G$, the maximum average degree $\operatorname{mad}(G)$ is the largest average degree of a nonempty subgraph of $G$. Hendrey, Norin and Wood asked whether this parameter is partitionable, that is, whether for all positive reals $a,b$ every graph $G$ with $\operatorname{mad}(G)<a+b$ admits a vertex pa...

Andrzej Grzesik, Lenka Kopfová, Gaurav Kucheriya et al. · 0 citations

Preprint Aug 2026

Maximal anti-Ramsey problems for posets

We study the forbidden poset analog of the maximal anti-Ramsey problem introduced for graphs by Burr, Erd\H os, Graham, and S\'os. For integers $m\le 2^n$ and poset $P=(P,\preceq)$, we introduce $\mathrm{ar_m}(n,m,P)$ (and $\mathrm{ar^*_m}(n,m,P)$) to denote the minimum integer $k$ such that there exists a family $\mat...

Binlong Li, Balázs Patkós, Chang-Xin Wang · 1 citation