Edge Colouring of Bipartite Graphs: Proving Valency Equality

[Stephane G]

Prove by induction on the number of edges in a graph that any bipartite graph has edge colouring number equal to its maximum valency. Also, Find such an edge colouring for a bipartite 4-regular cartesian or tensor product of your choice of 2-regular graphs

 

[chiro]

Prove by induction on the number of edges in a graph that any bipartite graph has edge colouring number equal to its maximum valency. Also, Find such an edge colouring for a bipartite 4-regular cartesian or tensor product of your choice of 2-regular graphs

Hey Stephane G and welcome to the forums.

For these kinds of questions, we ask that you show any working and any of your thinking before we help with these kinds of problems, since it is in the form of a homework problem (note it doesn't have to be a homework problem, just in the format of one).

What ideas do you have? What have you tried before?