Graph homomorphisms and chromatic numbers are foundational concepts in modern graph theory, with widespread applications that extend from combinatorial optimisation to theoretical computer science. A ...

The study of graph colouring has long been a central topic in discrete mathematics, with a prominent focus on optimising the assignment of labels or colours to vertices such that adjacent vertices are ...

Problem: How many colors are needed so that if each point in the plane is assigned one of the colors, no two points which are exactly distance 1 apart will be assigned the same color? This problem has ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...