Hi,
First, I cannot reproduce your issue when opening the resulting EPS files in Adobe Illustrator. Hence, the problem is probably not the exported file itself but the application you use to open it. Which software did you use?. Indeed, while I agree that there are multiple advantages to working with vector graphics export files, it is unfortunate that he recommended EPS which is an old format that is poorly interpreted even by specialized software like Adobe Illustrator. EMF files are a bit better, but you will learn that there are issues with transparency, text alignment, text fragment, and color conversion.
Therefore, if you absolutely need to export your graphs in vector format, I suggest exporting those as PDF files and editing them in a dedicated application like Adobe Illustrator.
However, if you are more interested in only preserving high-quality graphics for inclusion in presentations, posters, abstracts, or publications, I would suggest using a simple trick:
1) Copy the figure: CTLR + C
2) In the target document (Assuming you are on a Window system): Paste Special by pressing CTRL + ALT + V and choose Enhanced Metafile
This option maintains high resolution even when zooming in by 10X, but not that this format will not provide the high level of flexibility offered by vector graphics.
Best,
TS
Thierry R. Sornasse