Geodesic
Infinite families of tight regular tournaments
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 299-311.

Voir la notice de l'article provenant de la source Library of Science

In this paper, we construct infinite families of tight regular tournaments. In particular, we prove that two classes of regular tournaments, tame molds and ample tournaments are tight. We exhibit an infinite family of 3-dichromatic tight tournaments. With this family we positively answer to one case of a conjecture posed by V. Neumann-Lara. Finally, we show that any tournament with a tight mold is also tight.
Keywords: regular tournament, acyclic disconnection, tight tournament, mold, tame mold, ample tournament, domination digraph 
@article{DMGT_2007_27_2_a6,
     author = {Llano, Bernardo and Olsen, Mika},
     title = {Infinite families of tight regular tournaments},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {299--311},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a6/}
}
TY  - JOUR
AU  - Llano, Bernardo
AU  - Olsen, Mika
TI  - Infinite families of tight regular tournaments
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2007
SP  - 299
EP  - 311
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a6/
LA  - en
ID  - DMGT_2007_27_2_a6
ER  - 
%0 Journal Article
%A Llano, Bernardo
%A Olsen, Mika
%T Infinite families of tight regular tournaments
%J Discussiones Mathematicae. Graph Theory
%D 2007
%P 299-311
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a6/
%G en
%F DMGT_2007_27_2_a6
Llano, Bernardo; Olsen, Mika. Infinite families of tight regular tournaments. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 299-311. http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a6/

[1] J. 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.

[2] L.W. Beineke and K.B. Reid, Tournaments, in: L.W. Beineke, R.J. Wilson (Eds.), Selected Topics in Graph Theory (Academic Press, New York, 1979) 169-204.

[3] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (American Elsevier Pub. Co., 1976).

[4] S. Bowser, C. Cable and R. Lundgren, Niche graphs and mixed pair graphs of tournaments, J. Graph Theory 31 (1999) 319-332, doi: 10.1002/(SICI)1097-0118(199908)31:4319::AID-JGT7>3.0.CO;2-S

[5] H. Cho, F. Doherty, S-R. Kim and J. Lundgren, Domination graphs of regular tournaments II, Congr. Numer. 130 (1998) 95-111.

[6] H. Cho, S-R. Kim and J. Lundgren, Domination graphs of regular tournaments, Discrete Math. 252 (2002) 57-71, doi: 10.1016/S0012-365X(01)00289-8.

[7] D.C. Fisher, D. Guichard, J.R. Lundgren, S.K. Merz and K.B. Reid, Domination graphs with nontrivial components, Graphs Combin. 17 (2001) 227-236, doi: 10.1007/s003730170036.

[8] D.C. Fisher and J.R. Lundgren, Connected domination graphs of tournaments, J. Combin. Math. Combin. Comput. 31 (1999) 169-176.

[9] D.C. Fisher, J.R. Lundgren, S.K. Merz and K.B. Reid, The domination and competition graphs of a tournament, J. Graph Theory 29 (1998) 103-110, doi: 10.1002/(SICI)1097-0118(199810)29:2103::AID-JGT6>3.0.CO;2-V

[10] H. Galeana-Sánchez and V. Neumann-Lara, A class of tight circulant tournaments, Discuss. Math. Graph Theory 20 (2000) 109-128, doi: 10.7151/dmgt.1111.

[11] B. Llano and V. Neumann-Lara, Circulant tournaments of prime order are tight, (submitted).

[12] J.W. Moon, Topics on Tournaments (Holt, Rinehart Winston, New York, 1968).

[13] V. Neumann-Lara, The dichromatic number of a digraph, J. Combin. Theory (B) 33 (1982) 265-270, doi: 10.1016/0095-8956(82)90046-6.

[14] V. Neumann-Lara, The acyclic disconnection of a digraph, Discrete Math. 197/198 (1999) 617-632.

[15] V. Neumann-Lara and M. Olsen, Tame tournaments and their dichromatic number, (submitted).

[16] K.B. Reid, Tournaments, in: Jonathan Gross, Jay Yellen (eds.), Handbook of Graph Theory (CRC Press, 2004) 156-184.