Work

Proof of the mad conjecture and its coloring applications

Year: 2026

Type: preprint

Abstract: 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)

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.04645

Authors: Grzesik, Andrzej, Kopfová, Lenka, Kucheriya, Gaurav, Li, Binlong, Prorok, Magdalena

Institutions: Jagiellonian University, Institute of Science and Technology Austria, Charles University, Northwestern Polytechnical University, AGH University of Krakow

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

OpenAlex ID: W7220681263

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