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, ...

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 ...

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) ...