  We study a discrete diffusion process introduced in some combinatorial games
called FLOODIT and MADVIRUS that can be played online and whose computational
complexity has been recently studied by Arthur et al (FUN'2010). The flooding
dynamics used in those games can be defined for any colored graph. It has been
shown in a first report (in french, hal-00509488 on HAL archive) that studying
this dynamics directly on general graph is a valuable approach to understand
its specificities and extract uncluttered key patterns or algorithms that can
be applied with success to particular cases like the square grid of FLOODIT or
the hexagonal grid of MADVIRUS, and many other classes of graphs. This report
is the translation from french to english of the section in the french report
showing that the variant of the problem called 2-FREE-FLOOD-IT can be solved
with a polynomial algorithm, answering a question raised in the previous study
of FLOODIT by Arthur et al.
