Unmixed bipartite graphs

VILLARREAL, RAFAEL H.

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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.41 no.2 Bogotá July/Dec. 2007

Unmixed bipartite graphs

Grafos bipartitos sin mezcla

RAFAEL H. VILLARREAL¹

¹Centro de Investigación y de Estudios Avanzados del IPN, Ciudad de México, México. Email: vila@math.cinvestav.mx

Abstract

In this note we give a combinatorial characterization of all the unmixed bipartite graphs.

Key words: Unmixed graph, minimal vertex cover, bipartite graph, König theorem.

2000 Mathematics Subject Classification: 05C75, 05C90, 13H10.

Resumen

En esta nota nosotros presentamos una caracterización combinatoria de todos los grafos bipartitos no-mezcladas.

Palabras clave: Grafos no-mezclados, cubrimiento de vértices mínimo, grafos bipartitos, teorema de König.

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References

[1] Berge, C., Some common properties for regularizable graphs, edge-critical graphs and B-graphs, `Theory and practice of combinatorics´, Vol. 60, North-Holland Math. Stud., Amsterdam, Nederland, 1982, p. 31-44. [ Links ]

[2] Estrada, M. & Villarreal, R., `Cohen-Macaulay bipartite graphs´, Arch. Math. 68, (1997), 124-128. [ Links ]

[3] Harary, F., Graph Theory, Addison-Wesley, 1972. Reading, MA. [ Links ]

[4] Herzog, J. & Hibi, T., `Distributive lattices, bipartite graphs and Alexander duality´, J. Algebraic Combin. 22, 3 (2005), 289-302. [ Links ]

[5] Morey, S., Reyes, E. & Villarreal, R., Cohen-Macaulay, shellable and unmixed clutters with a perfect matching of König type. J. Pure Appl. Algebra. To appear. [ Links ]

[6] Plummer, M., `Some covering concepts in graphs´, J. Combinatorial Theory 8, (1970), 91-98. [ Links ]

[7] Ravindra, G., `Well-covered graphs´, J. Combinatorics Information Syst. Sci. 2, 1 (1977), 20-21. [ Links ]

[8] Villarreal, R., `Cohen-Macaulay graphs´, Manuscripta Math. 66, (1990), 277-293. [ Links ]

(Recibido en julio de 2007. Aceptado en agosto de 2007)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{Villarreal07,    

     AUTHOR = {Rafael H. Villarreal},    

     TITLE =  {{Unmixed bipartite graphs}},    

     JOURNAL =  {Revista Colombiana de Matemáticas},    

     YEAR =  {2007},    

     volume =  {41},    

     number =  {2},    

     pages =  {393-395}    

}