yEd relies completely on Java for retrieving font related information. Moreover, font support is inherently operating system dependent and known to be one of Java's weaker points.
Unfortunately, I do not know how the Java Runtime Environment (JRE) determines which of the fonts installed on a machine will be available for use.
However, when running yEd on an Oracle JRE (i.e. the JREs that are bundled with yEd), the following fonts are available on Linux, Mac OS X, and Windows:
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Dialog
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DialogInput
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Monospaced
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Serif
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SansSerif
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Lucida Bright
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Lucida Sans
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Lucida Sans Typewriter
So, for maximum cross-platform compatibility, you need to use one of these fonts. However, even if you do use one of the above fonts, there is no guarantee that the glyphs in these fonts are the same size on all platforms. In other words, even with those fonts, text sizes may very from Linux to Mac OS X to Windows.