The bright red sole used by Christian Louboutin on their shoes are protected by a US trademark. Colour Trade marks are mostly common with industrial goods like fiberglass insulation that must conform to strict regulatory standards, although many other industries also feature colour marks (for example Orange (Orange Brand Services Limited) with the colour Orange).
The Louboutin US trademark was registed in 2008, for red soled shoes and the colour red was claimed as a feature of the Trade mark, although
there was no limitation as to a particular shade of red.
However much recently a Manhattan judge held that Louboutin could not prevent Yves Saint Lauren (and other designers) from designing and selling red-soled shoes. The court held that the fashion industry is highly creative industry dependent on access to the full spectrum of colors. In this sector colour served “ornamental and aesthetic functions vital to robust competition”.
The position is yet to be tested in the UK where Louboutin owns a registered UK Trade mark, which was registered on grounds of acquired distinctiveness through use.
Further commentary can be found here(external website)