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 ...

This paper proves that for any integer n ≥ 4 and any rational number r, 2 ≤ r ≤ n — 2, there exists a graph G which has circular chromatic number r and which does not contain Kn as a minor. Journal ...