Graph colouring remains a central topic in graph theory, providing the mathematical framework for assigning colours to the elements of a graph under specific constraints. In particular, the colouring ...

A graph is planar if it can be drawn in the plane in such a way that no edges intersect, except of course at a common endvertex. Planar graphs corresponding to the regular polyhedra and other ...

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory. This past October, as Jacob Holm and Eva Rotenberg were thumbing through a ...

Let G be a graph and k a natural number. A k-coloring of G is a map c that maps the vertices of G into the set {1, 2, ..., k} (whose elements are called colors) such that no two adjacent vertices are ...

We prove that given any sequence $G_1, G_2,\ldots$ of graphs, where $G_1$ is finite planar and all other $G_i$ are possibly infinite, there are indices $i,j$ such ...

Let G = (V(G), E(G)) be a graph. A set S ⊆ E(G) is an edge k-cut in G if the graph G − S = (V(G), E(G) \ S) has at least k connected components. The generalized k-edge connectivity of a graph G, ...

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 ...

Statistical information is often shown using graphs and other diagrams. These can be easier to read than lists of numbers. You should be able to read and draw the following: The type of graph you use ...

Graphs are a useful way to show numerical data. There are a variety of graphs that can help highlight patterns and be used to reach conclusions. Choosing the right graph is very important. A bar chart ...