a) What does it mean that a simple graph is k-colorable (k > 1)? b) Define the lan- guage K-COLORING c) State the complexity theorems we have learnt on 2-COLORING and 3-COLORING. c) Is the following graph 3-colorable? Why? B-D-F A E a) Define what is meant by a language being NP-intermediate. b) State Ladner's Theorem on NP-intermediate languages. c) Is it known whether NP-intermediate languages exist? If your answer is no, explain why do you think so. If your answer is yes, name and define one of those languages if they exist.