Yellow/red/white composite connectors are rca cables with only the yellow carrying video. red and white for audio. You can only get standard def out of that yellow cable regardless of price or quality.
If you talk about the component cables (red, blue, green), your television will get analog high-definition video transmission, with a resolution until 1080i assuming that the actual connector has been built for it. In other words the CABLE itself can produce 1080i but can the CONNECTOR at the end of the cable carry 1080i...usually yes, but you never know what you might find in one of those dollar store cables