Prove that the property of being bipartite for a graph is recognizable.
Definition: A graphical parameter or graphical property is recognizable if for each graph $G$ of order at elast 3, it's possible to determine the value of the parameter for $G$ or whether $G$ has the property from the subgraph $G-v$, $v\in V(G)$
I'm not sure I understand the definition very well.
I know that bipartite graph doesn't contain odd cycle. I also know that for any bipartite graph of order $n$, then $m\leq \frac {n^2}{4}$.
Are these property enough to say the order and size of a bipartite are recognizable parameter?
Theorem 5.7: If $G$ is a graph of order $n \geq 3$ then $n$ and $m$ as well as degree of vertices of $G$ are determined from the $n$ subgraphs $G-v$, $v\in V(G)$
the book tells me from theorem 5.7, I can say that for the graph of order at least 3, the order, size and degree of its vertices are recognizable parameters. It also follow that the property of regular graph is recognizable because the degree of regularity is recognizable parameter.
For bipartite graph I think one of the property that is recognizable is you can color every vertex of the same part with the same color because they are not adjacent to each other, so every bipartite has at most 2 different color, right?