SVG, SVGZ, and PNG export have an option "Transparent Background" on tab "Image" in their export settings. If you select that option, you will get a fully transparent background in the exported file *no matter what background color is used in yEd*. I highly recommend using the aforementioned export setting with an opaque background for yEd's editor tabs because some export formats cannot handle transparency. E.g. JPEG does not support non-opaque pixels, which means that your original approach might result in broken image files.