The Erdős–Pósa property forms a pivotal concept in modern graph theory by establishing a profound duality between the problems of packing and covering cycles or other substructures. At its ...

Engineers could use this breakthrough in graph theory to design wildly efficient quantum computer chips.

We present an example of a result in graph theory that is used to obtain a result in another branch of mathematics. More precisely, we show that the isomorphism of certain directed graphs implies that ...

In theory, it cannot be ruled out that the algorithms might run for longer than the age of the universe. But in practice, many algorithms seem to work just fine.

Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.

Graph Theory, the bedrock of network science, has found extensive application in dissecting the attributes of complex networks, including those of the brain. It lays out a framework for examining ...