Carbohydrate in egg white
The one I found is Ovomucin,though it's not a pure carbohydrate.

Ovomucin is a highly glycosylated protein and approximately 33% of ovomucin is made up of carbohydrates.

Nutritional Values of Egg White Proteins paragraph of
http://ps.oxfordjournals.org/content/92/12/3292.full 
So you can see it's mostly a protein.

Ovomucin is a trypsin inhibitor found in raw egg white.
Ovomucin is responsible for the gel properties of fresh egg white and is believed to be involved in egg white thinning. Ovomucin is composed of two subunits:

α-ovomucin - carbohydrate-poor with a molecular mass of 254kDa

β-ovomucin - carbohydrate-rich with a molecular mass of 400-610kDa



Souce: Wikipedia