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2007 | 27 | 2 | 299-311
Tytuł artykułu

Infinite families of tight regular tournaments

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Tom
27
Numer
2
Strony
299-311
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-04-24
poprawiono
2006-11-14
zaakceptowano
2006-11-14
Twórcy
  • Departamento de Matemáticas, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, Colonia Vicentina, 09340, México, D.F.
autor
  • Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana, Cuajimalpa, Prolongación Canal de Miramontes 3855, Colonia Ex-Hacienda San Juan de Dios, 14387, México, D.F.
Bibliografia
  • [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)31:4<319::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)29:2<103::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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1362
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