Graph Coloring Problem : How to Think About Algorithms Exer 1.6.2
You're right that the statement is false. The correct statement states that every undirected simple graph in which each node has at most $d$ neighbors can be colored using $d+1$ colors so that each edge connects nodes having different color. Stated in more idiomatic language, every undirected simple graph of maximum degree $d$ can be (properly) colored using $d+1$ colors.