In a TigerVNC session:
1. Use cvt to generate a new modeline (in this case, for 3840
x 2160 x 60 Hz-- you can always specify 60 Hz with VNC):
  $ cvt 3840 2160 60
  # 3840x2160 59.98 Hz (CVT 8.29M9) hsync: 134.18 kHz; pclk:
712.75 MHz
Modeline "3840x2160_60.00"Â 712.75Â 3840 4160 4576 5312Â 2160
2163 2168 2237 -hsync +vsync
2. Create a new mode with that modeline.
  $ xrandr --newmode "3840x2160" 712.75 3840 4160 4576 5312 2160 2163 2168 2237 -hsync +vsync
3. Add the new mode.
  $ xrandr --addmode VNC-0 3840x2160
4. Verify that the new mode was added.
  $ xrandr
  Screen 0: minimum 32 x 32, current 1024 x 768, maximum 32768
x 32768
  VNC-0 connected 1024x768+0+0 0mm x 0mm
   1024x768     60.00*+
   1920x1200    60.00Â
   1920x1080    60.00Â
   1600x1200    60.00Â
   1680x1050    60.00Â
   1400x1050    60.00Â
   1360x768     60.00Â
   1280x1024    60.00Â
   1280x960     60.00Â
   1280x800     60.00Â
   1280x720     60.00Â
   800x600      60.00Â
   640x480      60.00Â
   3840x2160    59.98Â
5. Select the new mode.
  $ xrandr -s 3840x2160
  $ xrandr
  Screen 0: minimum 32 x 32, current 3840 x 2160, maximum 32768
x 32768
  VNC-0 connected 3840x2160+0+0 0mm x 0mm
   1024x768     60.00 +
   1920x1200    60.00Â
   1920x1080    60.00Â
   1600x1200    60.00Â
   1680x1050    60.00Â
   1400x1050    60.00Â
   1360x768     60.00Â
   1280x1024    60.00Â
   1280x960     60.00Â
   1280x800     60.00Â
   1280x720     60.00Â
   800x600      60.00Â
   640x480      60.00Â
   3840x2160    59.98*
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Yes, VNC-0 is the name of the virtual display for the first virtual screen. If there are multiple Xinerama screens, then you might also have VNC-1. Those display names are VNC-specific. (TurboVNC also uses the same convention.)
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