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Several results on chordal bipartite graphs
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 4, pp. 577-583 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 05C38, 05C50, 05C75, 15A06 
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Bakonyi, Mihály; Bono, Aaron. Several results on chordal bipartite graphs. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 4, pp. 577-583. http://geodesic.mathdoc.fr/item/CMJ_1997_47_4_a0/

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