Well, you can try printing directly from yEd instead of exporting your diagram to some graphics format first.
If you export to PDF (or some other graphics format) first and then print the exported document, the result of the printout does not really depend on yEd anymore. (After all, you are not using yEd for printing in this use case.) The printout quality does depend on your actual printer/plotter, the corresponding driver software, and the PDF viewer application used for printing.
That said, if you print a 2448px raster image (i.e. JPG, PNG) on 34in you have an effective resolution of 72dpi. That is acceptable on screen (even though most modern displays use 96dpi), but is very low for a printout. For good results, you will probably need something around 300dpi which means 10200px for 34in. (Unless there are embedded raster images, this rule does not apply to vector graphics like PDF and SVG, though.)