On scores in tournaments

T. A. Naikoo

doi:10.2478/ausi-2018-0013

Abstract

A tournament is an orientation of a complete simple graph. The score of a vertex in a tournament is the outdegree of the vertex. In this paper, we obtain various results on the scores in tournaments.

References

[1] P. Avery, Score sequences of oriented graphs, J. Graph Theory, 15, 3 (1991) 251–257. ⇒25710.1002/jgt.3190150303
Search in Google Scholar Back to article
[2] R. A. Brualdi and J. Shen, Landau’s inequalities for tournament scores and a short proof of a Theorem on transitive sub-tournaments, J. Graph Theory, 38 (2001) 244–254. ⇒25810.1002/jgt.10008
Search in Google Scholar Back to article
[3] R. A. Brualdi and J. Shen, Landau’s inequalities for tournament scores and a short proof of a Theorem on transitive sub-tournaments, J. Graph Theory, 38 (2001) 244–254. ⇒25810.1002/jgt.10008
Search in Google Scholar Back to article
[4] J. R. Griggs and K. B. Reid, Landau’s theorem revisited, Australasian J. Combinatorics, 20 (1999) 19–24. ⇒258
Search in Google Scholar Back to article
[5] K. K. Kayibi, M. A. Khan and S. Pirzada, Uniform sampling of khypertournaments, Linear and Multilinear Algebra, 61, 1 (2012) 123–138. ⇒25710.1080/03081087.2012.664771
Search in Google Scholar Back to article
[6] M. A. Khan, S. Pirzada and K. K. Kayibi, Scores, inequalities and regular hypertournaments, J. Math. Ineq. Appl., 15, 2 (2012) 343–351. ⇒25710.7153/mia-15-28
Search in Google Scholar Back to article
[7] H. G. Landau, On dominance relations and the structure of animal societies, III, the condition for a score structure, Bull. Math. Biophys., 15 (1953) 143–148. ⇒257, 25810.1007/BF02476378
Search in Google Scholar Back to article
[8] J. W. Moon, Topics on Tournaments, Holt, Rinehart and Winston, New York (1968). ⇒258
Search in Google Scholar Back to article
[9] S. Pirzada and G. Zhou, Score sequences in oriented k-hypergraphs, European J. Pure and Applied Mathematics, 1, 3 (2008) 10–20. ⇒257
Search in Google Scholar Back to article
[10] S. Pirzada, T. A. Chishti and T. A. Naikoo, Score lists in [h-k]-bipartite hyper-tournaments, Discrete Mathematics and Applications, 19, 3 (2009) 321-328. ⇒25710.1515/DMA.2009.020
Search in Google Scholar Back to article
[11] S. Pirzada and G. Zhou, New proof on k-hypertournament scores, Acta Univ. Sapientiae, Informatica, 2, 1 (2010) 5–9. ⇒257
Search in Google Scholar Back to article
[12] S. Pirzada, On scores in multipartite hypertournaments, Eurasian Math. J.2, 1 (2011) 112–119. ⇒257
Search in Google Scholar Back to article
[13] S. Pirzada, On scores in bipartite hypertournaments, Math. Vesnik, 64,4 (2012) 286-296. ⇒257
Search in Google Scholar Back to article
[14] S. Pirzada, G. Zhou and A. Ivanyi, Score lists of multipartite hypertournaments, Acta Univ. Sapien. Informatica, 2, 2 (2010) 184–193. ⇒257
Search in Google Scholar Back to article
[15] S. Pirzada, An Introduction to Graph Theory, Universities Press, Hyderabad, India, 2012. ⇒257
Search in Google Scholar Back to article
[16] S. Pirzada, T. A. Naikoo and Zhou Guofei, Score lists in tripartite hypertournaments, Graphs and Combinatorics, 23, 4 (2007) 445-454. ⇒25710.1007/s00373-007-0735-y
Search in Google Scholar Back to article
[17] K. B. Reid, Tournament, scores, kings, generalizations and special topics, Congressus Numerantium, 115 (1996) 171–211. ⇒258
Search in Google Scholar Back to article
[18] S. Pirzada and T. A. Naikoo, Inequalities for marks in digraphs, J. Math. Inequalities Appl., 9, 2 (2006) 189–198. ⇒25710.7153/mia-09-19
Search in Google Scholar Back to article
[19] S. Pirzada and U. Samee, Mark sequences in digraphs, Seminare Lotharingien de Combinatoire, 55 (2006) Art.B55c. ⇒257
Search in Google Scholar Back to article
[20] S. Pirzada and T. A. Naikoo, Score sets for oriented graphs, Applicable Analysis and Discrete Mathematics, 2, 1 (2008) 107–113. ⇒25710.2298/AADM0801107P
Search in Google Scholar Back to article
[21] S. Pirzada and T. A. Naikoo, Score sets in k-partite tournaments, J. Applied Mathematics and Computing, 22, 1-2 (2006) 237–245. ⇒25710.1007/BF02896474
Search in Google Scholar Back to article
[22] S. Pirzada, T. A. Naikoo and T. A. Chishti, Score sets in oriented bipartite graphs, Novi Sad J. Mathematics, 36, 1 (2006) 35–45. ⇒25710.1007/BF02831973
Search in Google Scholar Back to article
[23] S. Pirzada, T. A. Naikoo and N. A. Shah, Score sequences in oriented graphs, J. Applied Mathematics and Computing, 23, 1-2 (2007) 257–268. ⇒25710.1007/BF02831973
Search in Google Scholar Back to article
[24] S. Pirzada and T. A. Naikoo, Score sets in tournaments, Vietnam J. Math., 34, 2 (2006) 157–161. ⇒25710.1007/BF02831973
Search in Google Scholar Back to article
[25] Zhou Guofei and S. Pirzada, Degree Sequences in oriented k-hypergraphs, J. Applied Math. and Comput., 27 (2008) 149–158. ⇒25710.1007/s12190-008-0047-2
Search in Google Scholar Back to article

On scores in tournaments

Abstract

Paradigm

My account