Question: Please explain each step in detail, thanks! 8. [8 marks] A 2-colouring of an undirected graph with n vertices and m edges is the assignment

Please explain each step in detail, thanks!

8. [8 marks] A 2-colouring of an undirected graph with n vertices and m edges is the assignment of one of two colours (say, black or white) to each vertex of the graph, so that no two adjacent nodes have the same colour. So, if there is an edge (u,v) in the graph, either node u is black and v is white or vice versa. Give (pseudocode!) an O(n+m) time algorithm to 2-colour a graph or determine that no such colouring exists, and justify the running time. The following shows examples of graphs that are and are not 2-colourable

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