On the bipartite vertex frustration of graphs

The bipartite vertex (resp. edge) frustration of a graph G, denoted by ψ(G) (resp. ϕ(G)), is the smallest number of vertices (resp. edges) that have to be deleted from G to obtain a bipartite subgraph of G. A sharp lower bound of the bipartite vertex frustration of the line graph L(G) of every graph G is given. In addition, the exact value of ψ(L(G)) is calculated when G is a forest.