I was learning algorithms and data structures, and can't manage with this problem:
We say that a graph is triangular when it is undirected, connected and it's each biconnected component is a cycle of length $3$.
a) Prove that each triangular graph is $3$-colorable (in terms of coloring vertices, of course).
b) Suggest an effective algorithm for $3$-coloring of a triangular graph.
c) Suggest an effective algorithm for finding maximum matching in triangular graphs.
I think a) can be approached with induction, but tried and I don't see it. For b) and c) no idea. Can anybody help? I really want to finally solve some graph theory problems, but they are so hard.