Zobecnění magických ohodnocení a jejich využití při losování sportovních turnajů

Abstract

This bachelor thesis deals with magic labeling. The thesis summarizes basic types of the magic labeling, the most important results, and presents clear examples of the labeling when planning sports tournaments. It also provides new results in a form of the generalized handicap labeling where a so-called modified handicap labeling is introduced which naturally removes the requirement of the arrangement of vertex labels into an arithmetic progression {1,2,...,n}, even also for graphs which have labels arranged in the progression {1,2,...,n/2}U{(n+4/2,...,n+1}. The existence of labeling for 2-regular graph class is completely settled for the newly defined vertex labeling.