Simple score sequences

• Main Author: Mariquit, Tito Macasero
• Format: text
• Language: English
• Published: Animo Repository 1997
• Subjects: Graph theory; Mathematics > Formulae; Sequences (Mathematics); Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/1863; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/8701/viewcontent/TG02711_F_Partial.pdf
• Institution: De La Salle University

This is a treatise of the article by P. Avery on the condition for a tournament score sequence to be simple. This study establishes the detailed proof of the more important result by giving the basic concepts, definitions, lemmas and theorems with their corresponding proofs and examples. The condition is given for a tournament score sequence to belong to exactly one tournament. The major results is that if a score sequence S is simple then every strong component of S is one of 0, 1,1,1, 1,1,2,2, or 2,2,2,2. Moreover, if every strong component is one of these, then S must be simple.