Graphs are collections of vertices (dots) connected by edges (lines). After hundreds of years of study, mathematicians are still investigating their basic properties. One concerns the “parity” of a ...

Doing this would divide a set of n vertices into two subsets, and one of those subsets would have to contain at least half the vertices. This guarantees that every graph has an even subgraph that’s at ...

Gallai–Ramsey number: The minimum number of vertices in a complete graph such that every Gallai colouring using a given number of colours yields a monochromatic copy of a specified subgraph.