G is a graph and B is a spanning bipartite subgraph of G such that B=B(X,Y) and v is any vertex in G My work: I know that $d_B(v)=|N_B(v)|$ So we have to prove that $N_B(v)=N_G(v)\cap Y$ It's clear that $N_B(v)\supseteq N_G(v)\cap Y$ is always true I tried to prove the second direction by contradiction and I got $\exists vy\in E(G),y\in Y/vy\notin E(B)$
What should I do next ? Thanks in advance