Does X-Windows have to be installed on a Linux-box in order for Java to display fullscreen graphics?
To really display something graphical on the screen, yes. Bud there is a headless version of the JRE for just running it. You won't see any graphical output, but it will run. Alternatively, you can log in remotely and use X forwarding to run the java code on the server but let the client handle displaying graphics.