Graph colouring is a fundamental problem in both theoretical and applied combinatorics, with significant implications for computer science, operational research and network theory. At its essence, ...

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 ...

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 ...

Vol. 12, No. 4, Dedicated to Professor Ko-Wei Lih on the Occasion of His 60th Birthday (July 2008), pp. 997-1005 (9 pages) The circular chromatic number χc(G) of a graph G is a very natural ...

Let p be a positive real number and S(p) the circle in the plane with circumference p. A subset U of S(p) is said to be assignable if it is the union of finitely many open arcs on S(p). Let length(U) ...