Colouring Graphs

[Jon Perry]

'> If we have a graph with the edges coloured with no rules, what colouring
are
> allowed for the vertices such that if n vertices have the same coloured
edge
> in common, then they must be coloured differently?'

"Are you saying: (1) If M = set of all vertices which have an m-coloured
edge adjacent to them, all all vertices in M must be coloured differently.
Or (2) If M = set of all vertices on *one* specific coloured edge, then
all vertices in M must be coloured differently. ?"

Given a vertex V, let M(c) be the set of vertices adjacent to V along an
edge of colour c.

Each vertex in M(c) must be a different colour to V.

Jon Perry
perry at globalnet.co.uk
http://www.users.globalnet.co.uk/~perry/maths/
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