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 ...

Let G be an outerplanar graph with maximum degree Δ (G) ≥ 3. We prove that the chromatic number χ (G²) of the square of G is at most Δ (G) + 2. This confirms a conjecture of Wegner [8] for outerplanar ...

Simulated annealing is a randomized technique proposed by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi for improving local optimization algorithms. Here we report on experiments at adapting simulated ...

From here graph theory got expanded and generalized into relations between objects, finding use in fields from computer science and chemistry to biology and linguistics.

Abstractions blog A New Algorithm for Graph Crossings, Hiding in Plain Sight Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory ...

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