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Several results on chordal bipartite graphs

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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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References

  1. M. Bakonyi: Completion of Partial Operator Matrices. Thesis, The College of William and Mary, Williamsburg, Virginia, August, 1992.

  2. M. Bakonyi, T. Constantinescu: Inheritance Principles for Chordal Graphs. Linear Algebra Appl. 148 (1991), 125–143.

    Google Scholar 

  3. N. Cohen, C.R. Johnson, L. Rodman, H. Woerdeman: Ranks of Completions of Partial Matrices, in: The Gohberg Anniversary Collection, Vol I (Eds. H. Dym. S. Goldberg, M.A. Kaashoek and P. Lancaster). Operator Theory: Adv. Appl., OT 40, Birhäuser Verlag, Basel, 1989, pp. 165–185.

    Google Scholar 

  4. M.C. Golumbic: Algorithmic Graph Theory and the Perfect Graph. Academic Press, New York, 1980.

    Google Scholar 

  5. M.C. Golumbic, C.F. Goss: Perfect Elimination and Chordal Bipartite Graphs. J. Graph Theory 2 (1978), 155–163.

    Google Scholar 

  6. R. Grone, C.R. Johnson, E. Sa, H. Wolkowitz: Positive Definite Completions of Partial Hermitian Matrices. Linear Algebra and Appl. 58 (1984), 102–124.

    Google Scholar 

  7. C.R. Johnson, L. Rodman: Completion of Partial Matrices to Contractions. J. Functional Analysis 69 (1986), 260–267.

    Google Scholar 

  8. D.J. Rose: Triangulated Graphs and the Elimination Process. J. Math. Anal. Appl. 32 (1970), 597–609.

    Google Scholar 

  9. D.J. Rose, R.E. Tarjan, G.S. Leuker: Algorithmic Aspects of Vertex Eliminations on Directed Graphs. SIAM J. Appl. Math. 34 (1978), 176–197.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Georgia State University, University Plaza, Atlanta, GA, 30303

    Mihály Bakonyi

  2. Department of Mathematics, University of Missouri, Columbia, Missouri, 65211, U.S.A

    Aaron Bono

Authors
  1. Mihály Bakonyi
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  2. Aaron Bono
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Bakonyi, M., Bono, A. Several results on chordal bipartite graphs. Czechoslovak Mathematical Journal 47, 577–583 (1997). https://doi.org/10.1023/A:1022806215452

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  • DOI: https://doi.org/10.1023/A:1022806215452

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