I have an idea: SVG!
In SVG, polygons are easy.
http://www.w3schools.com/svg/tryit.asp?filename=polygon2&type=svg
Filling with color: trivial.
See this SVG game written in SVG:
http://www.codedread.com/yastframe.php
Mapserver knows the SVG format.
http://mapserver.org/output/svg.html
Filling areas (or circles, representing graph nodes) with the player's color: would be easy.
(I cannot help more, sorry. I am not an SVG expert.)
