Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a public transportation network. Mathematicians have long sought to develop ...

Graph connectivity and Hamiltonian properties lie at the heart of both theoretical combinatorics and practical network design. Connectivity quantifies the robustness of a network by the minimum number ...

In algorithms, as in life, negativity can be a drag. Consider the problem of finding the shortest path between two points on a graph — a network of nodes connected by links, or edges. Often, these ...

Graph colouring, the assignment of colours to the vertices of a graph so that no two adjacent vertices share the same colour, represents a canonical NP-hard combinatorial optimisation problem with ...

The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...