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 core, this ...

Let G be a directed graph such that every edge e of G is associated with a positive integer, called the index of e. Then G is called a network graph if, at every vertex v of G, the sum of the indices ...

Research in group theory has long embraced equations as a means to elucidate the structure and behaviour of groups. In particular, Diophantine problems—those surrounding the existence and ...

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...

Researchers thought that they were five years away from solving a math riddle from the 1980's. In reality, and without knowing, they had nearly cracked the problem and had just given away much of the ...

Quantum walk applications are divided into 4 main categories: quantum computing, quantum simulation, quantum information processing, and graph-theoretic applications. Quantum walks are a powerful ...