TITLE: Are the graphs with no vertex and 1 vertex bipartite?
QUESTION [8 upvotes]: I am not sure how the definition of bipartite graph fits for these graphs. If they are bipartite where is the bipartition?

REPLY [2 votes]: A graph with no edges and 1 or n vertices is bipartite.
Mistake: It is very common mistake as people think that graph must be connected to be bipartite.
Correction: No it is not the case, as graph with no edges will be trivially bipartite.
Mistake: If graph has no circuits then it cannot be bipartite as all circuits must be of even length to make graph bipartite.
Correction: If graph have no circuits (means graph have 0 circuit so it also even number), so again by definition of bipartite graph it will be bipartite.