To detect your yellow, you need to find the relationship between the RGB channels that creates a yellow colour. Now, pure yellow is where the red and green channels are equal and the blue channel is zero.
Unfortunately, this is not likely to be the case in your image. What you'll find is that for the yellow parts, your red and green channels are 'roughly similar', and the blue channel is just about anything (as the blue channel value increases, the yellow becomes more saturated (as the RGB triple approaches a gray value). As the red and green diverge, the colour becomes more orange or lime.
So there's no 'yes/no' logical value that will tell you what to do, but if you try creating one you'll end up with jagged edges, colour bleeding, or both.
What you want is to devise a 'fuzzy truth' value which is 1 for pure yellow, and drops to zero as it becomes less yellow. You calculate that for each pixel (it'll be a single vector operation on your image data), and then use it to blend between the gray image and the colour image.
graypic = rgb2gray(pic);
isyellow = ...
pic = isyellow .* pic + (1-isyellow) .* graypic;
I don't have the image processing toolbox so I can't check rgb2gray. You may need to use repmat and possibly reshape to make it the same dimension as your pic. Do the same with your isyellow selector.
Speaking of the selector...
You need to work out a formula for how yellow something can be. I would start by taking those r, g, and b splits you have already shown, and doing something like this:
isyellow = (1 - abs(r-g)) * (r+g - 2*b);
This gives a maximum value when r and g are similar and large, and when the blue value is furthest from the average of r and g. I would probably also scale the result by some gaussian and clip it between 0 and 1.
