Graph Coloring Note that χ(G) denotes the chromatic number of graph G, Kn denotes a complete graph on n vertices, and Km,n denotes the complete bipartite graph in which the sets that bipartition the...

Graph Coloring
Note that χ(G) denotes the chromatic number of graph G, Kn
denotes a complete graph on n vertices, and Km,n denotes the complete bipartite graph in
which the sets that bipartition the vertices have cardinalities m and n, respectively.

(c) Compute χ(K3,3). Justify your answer with complete details and complete sentences.

(d) For n, m ∈ N, compute χ(Km,n). Do not justify your work.

(e) Give an example of a graph G whose chromatic number is 3, but that contains no K3

as a subgraph