Let G=(V,E) be a connex graph. Color it's edges randomly with red/blue.
-prove that there exists an Eulerian circuit, without any two adjacent edges of the same color.. only if for any
v vertex of G the number of incident blue edges is equal to the number of red ones.
-if G is complete and
x,y,z are three distinct vertices prove that, if there is a path without consecutive edges of the same color from
y passing through
z, then there is a path with the same property that has
xz as the first edge or
zy as the last edge.
Please help me by at least providing some suitable references that may help me solve this problem.
Thank you in advance.