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.