Math + CS = 11

Google’s favicon has bothered me for a little while now – not because it looks bad, but because it uses five colors.

In graph theory, it is not very difficult to prove that any planar graph is five colorable. One proof of the theorem relies on the fact that if a graph is a K­₅ it is non-planar. Thus, at least one vertex must not be adjacent to a second and you can alternate between the colors of those two vertices to do the rest of the graph.

In Google’s main logo as seen on google.com, the logo uses blue, red, yellow, and green. Four colors. So far, so good. When you look at the favicon, they use blue, red, yellow, green, and white. Five colors. Some may argue that the white shouldn’t be counted because it is the background color, but I believe that when a logo needs the background as much as it does in Google’s favicon (without it there wouldn’t be a ‘g’) it should be counted.

The logo could easily be adjusted as to only use four colors. For example, the blue parts could be colored red and the white could be changed to blue. Or following along with the use of two blue parts and two red parts in Google’s main logo, the green color be yellow, the yellow in the g could be red and the g could be colored green instead of white. Problem solved.

Even the main logo could also be changed to accommodate for the white background either by changing the color of the ‘o’ or ‘l’ to blue or red and leaving the background white or the background could be changed to the original color of the ‘o’ or ‘l’.

</rant>