Prove: “The complement of the graph G is an Eulerian graph whenever G is also  an Eulerian graph of odd order and the complement of G is connected.” Give a figure and details to validate the proof.

I tried asking this in seperate questions but no body answered . b) Prove that G = K2,12 is planar by drawing G without any edge crossings. (c) Give an example of a graph G whose chromatic number is 3, but that contains no K3 as a subgraph. You must prove that your graph actually has chromatic number 3.

Prove that every graph G on {1,...n} which is acyclic and has n – 2 edges has exactly 2 connected components.

A planar connected graph, G, is 2-colorable on its faces if and only if G is an Eulerian graph. True or False?