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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 43906 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Mahmoodian, Ebadollah
- Abstract:
- The concept of defining set in matching theory, recently has been taken into consideration by chemists and mathematicians because of several important applied problems in chemistry and mathematics. This concept is studied extensively in vari-ous areas of combinatorics and graph theory. The idea is to obtain total combinatorial structure of one object uniquely, based on some special information about it. Defin-ing set has been studied in various areas of graph theory like colouring, matching , orientations of graphs and etc. and many researches have been done in these areas. What we focus on, in this thesis is the defining set in matching theory that has been called “forcing set”. A minimum forcing set of a perfect matching M of a graph, is a subset of M of minimum size that determines M uniquely. In other words, it is contained in no other perfect matching except M. The smallest forcing set of a graph is a forcing set with smallest size between all perfect matchings of G.
Global forcing set is a new concept that has been proposed recently and is a kind of generalizations from the concept of forcing set. This concept presents global prop-erties throughout all perfect matchings simultaneously and not just to one specific perfect matching. In this thesis, we have collected all the main researches and results that have been done in this area and then present some new results about it. Finally, we list some open problems about this subject - Keywords:
- Graphs ; Perfect Matching ; Defining Set ; Forcing Sets ; Computational Complexity ; Global Forcing Set
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