There is no need to cut yarn between color changes when knitting colorwork or stripes. Carrying yarn up the side of your work allows you to bring the different colors discreetly up the edge. Consistency is the key to a professional edge and this video will guide you to expert color changing.
Double Ended Knitting (Stripes)
This technique allows for single rows of striping in flat knitting without having to turn the work at the end of the row. A circular or double pointed needle is all that is needed to try this simple method for color work.