Papers for

software developers working on graph algorithms

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Every graph with enough connections must contain all small trees

The Erdős--Sós Theorem

Abstract: We present an exposition of a proof, discovered by GPT-6 Astra, of the Erdős--Sós Conjecture, which states that every graph with average degree greater than $t-2$ contains every tree on $t\geq 2$ vertices.

Tue 15 SeptDiscrete Mathematics

The gist

The paper explains a mathematical proof for a long-standing idea about networks, called the Erdős--Sós Conjecture. This idea says that if a network has enough connections on average, it will always include every kind of tree-shaped sub-network of a certain size. The authors show that when the average number of connections is higher than a specific threshold, every tree with that many points is guaranteed to be inside. This proof was discovered using a powerful AI called GPT-6 Astra.

Open → 2609.17877v1