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California State University – San Bernardino

1. Alshaikh, Rana Ali. Upset Paths and 2-Majority Tournaments.

Degree: MAin Mathematics, Mathematics, 2016, California State University – San Bernardino

In 2005, Alon, et al. proved that tournaments arising from majority voting scenarios have minimum dominating sets that are bounded by a constant that depends only on the notion of what is meant by a majority. Moreover, they proved that when a majority means that Candidate A beats Candidate B when Candidate A is ranked above Candidate B by at least two out of three voters, the tournament used to model this voting scenario has a minimum dominating set of size at most three. This result gives 2-majority tournaments some significance among all tournaments and motivates us to investigate when a given tournament can be considered a 2-majority tournament. In this thesis, we prove, among other things, that the presence of an upset path in a tournament allows us to conclude the tournament is realizable as a 2-majority tournament. Advisors/Committee Members: Jeremy Aikin.

Subjects/Keywords: upset paths; 2-majority tournaments; UP-sets.; Discrete Mathematics and Combinatorics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Alshaikh, R. A. (2016). Upset Paths and 2-Majority Tournaments. (Thesis). California State University – San Bernardino. Retrieved from http://scholarworks.lib.csusb.edu/etd/356

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Alshaikh, Rana Ali. “Upset Paths and 2-Majority Tournaments.” 2016. Thesis, California State University – San Bernardino. Accessed October 21, 2019. http://scholarworks.lib.csusb.edu/etd/356.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Alshaikh, Rana Ali. “Upset Paths and 2-Majority Tournaments.” 2016. Web. 21 Oct 2019.

Vancouver:

Alshaikh RA. Upset Paths and 2-Majority Tournaments. [Internet] [Thesis]. California State University – San Bernardino; 2016. [cited 2019 Oct 21]. Available from: http://scholarworks.lib.csusb.edu/etd/356.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Alshaikh RA. Upset Paths and 2-Majority Tournaments. [Thesis]. California State University – San Bernardino; 2016. Available from: http://scholarworks.lib.csusb.edu/etd/356

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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