Graph List Coloring

Hi
please can someone help me for this algorithm.
The problem is the classic graph coloring with the condition: two adjacent nodes do not have the same color and any vertix has a list of admitted colors.
thanks a lot

Hi
please can someone help me for this algorithm.
The problem is the classic graph coloring with the
condition: two adjacent nodes do not have the same
color and any vertix has a list of admitted colors.
thanks a lotThis is related to the map colouring problem. If you draw
a link between the capital cities of each pair of countries
with a common border, you get a graph. Conversely the graph
gives rise to a map.
Therefore, the literature on map colouring could be helpful.
The fact that each vertex has a list of admissible colours is
a complication that could prevent any solution from existing.
For example, if two vertices have only one admissible colour,
the same for each, then it can't be done. The famous four
colour theorem, first proved by Appel and Haaken in the 1970s
(using a computer intensive proof) shows that a colouring is
always possible if all vertices have the same list of four
colours, but it was known long before that if there are only
three colours, there are maps that can't be coloured.
Obviously, an exhaustive search would work in theory, but it
would at least be an exponential time algorithm.
Start with one colour for any vertex and choose a different
colour for each adjacent vertex. Then do the same for each of
the newly coloured vertices, skipping those that have already
been coloured. Keep going until a vertex can't be coloured or
the whole graph has been coloured.
Each time you get stuck, backtrack and change a colour until
you've tried every colour on each list, or you find a colouring.
Hopefully there's a more efficient algorithm in the literature.

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