Discussiones
Mathematicae Graph Theory 20(1) (2000) 109-128
DOI: https://doi.org/10.7151/dmgt.1111
A CLASS OF TIGHT CIRCULANT TOURNAMENTS
Hortensia Galeana-Sánchez and Víctor Neumann-Lara
Instituto de Matemáticas, UNAM
Area de la Investigación Científica
Ciudad Universitaria
04510, México, D.F., MEXICO
e-mail: hgaleana@matem.unam.mx
e-mail: neumann@matem.unam.mx
Abstract
A tournament is said to be tight whenever every 3-colouring of its vertices using the 3 colours, leaves at least one cyclic triangle all whose vertices have different colours. In this paper, we extend the class of known tight circulant tournaments.
Keywords: Circulant tournament, acyclic disconnection, vertex 3-colouring, 3-chromatic triangle, tight tournament.
1991 Mathematics Subject Classification: 05C20, 05C15.
References
| [1] | B. Abrego, J.L. Arocha, S. Fernández Merchant and V. Neumann-Lara, Tightness problems in the plane, Discrete Math. 194 (1999) 1-11, doi: 10.1016/S0012-365X(98)00031-4. |
| [2] | J.L. Arocha, J. Bracho and V. Neumann-Lara, On the minimum size of tight hypergraphs, J. Graph Theory 16 (1992) 319-326, doi: 10.1002/jgt.3190160405. |
| [3] | J.L. Arocha, J. Bracho and V. Neumann-Lara, Tight and untight triangulated surfaces, J. Combin. Theory (B) 63 (1995) 185-199, doi: 10.1006/jctb.1995.1015. |
| [4] | J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (American Elsevier Pub. Co., 1976). |
| [5] | V. Neumann-Lara, The acyclic disconnection of a digraph, Discrete Math. 197-198 (1999) 617-632. |
| [6] | V. Neumann-Lara and M.A. Pizana, Externally loose k-dichromatic tournaments, in preparation. |
Received 25 August 1999
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