Several results on chordal bipartite graphs
Mihály Bakonyi, Aaron Bono · Czechoslovak Mathematical Journal · 1997
The question of generalizing results involving chordal graphs to similar concepts for chordal bipartite graphs is addressed. First, it is found that the removal of a bisimplicial edge from a chordal bipartite graph produces a chordal bipartite graph. As consequence, occurance of arithmetic zeros will not terminate perfect Gaussian elimination on sparse matrices having associated a chordal bipartite graph. Next, a property concerning minimal edge separators is presented. Finally, it is shown that, to any vertex of a chordal bipartite graph an edge may be added such that the chordality is maintained.