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 distance graph shows the height of a plane as it completes a journey. When the plane is at a height of 38,000 feet (ft), it travels at a constant speed of 550 miles per hour. The question asks how ...

Real life situations such as travelling over time and across distance can be drawn on a graph. Exact distances and times are plotted on the graph. These are shown as co-ordinates. These points are ...

If true, the following conjecture of Thomassen [Th81] is a planarity criterion for a special class of graphs that involves only K 5. Recall that a planar graph on n vertices contains at most 3n-6 ...