Several results on chordal bipartite graphs |
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| Authors: | Mihály Bakonyi Aaron Bono |
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| Institution: | (1) Department of Mathematics, Georgia State University, University Plaza, Atlanta, GA, 30303;(2) Department of Mathematics, University of Missouri, Columbia, Missouri, 65211, U.S.A |
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| Abstract: | 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. |
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