Numbering Code	U-ENG29 29030 LJ10	Year/Term	2022 ・ Second semester
Number of Credits	2	Course Type	Lecture
Target Year		Target Student
Language	Japanese	Day/Period	Thu.4
Instructor name	KAWAHARA JUN (Graduate School of Informatics Associate Professor)
Outline and Purpose of the Course	We learn basic theories of graphs and their applications, and fundamental algorithms for solving graph problems.
Course Goals	The goal of this course is to learn basic theories of graphs and their applications, and fundamental algorithms for solving graph problems.
Schedule and Contents	1. Foundations of Graphs and (4 timeslots) I explain definition of graphs and basic properties of graphs. I also briefly review the basics of algorithms and their complexity. 2. Minimum spanning trees (1 timeslot) Kruskal's algorithm, Prim's algorithm, Steiner tree problem. 3. Shortest path problems (1 timeslot) Dijkstra's algorithm. 4. Eurer circuits and Hamiltonian cycles (2 timeslots) Eurer circuits, Hamiltonian cycles, Dirac's theorem. Ore's theorem. 5. Graph coloring (2 timeslots) Vertex coloring and edge coloring. Brooks's theorem, Vizing's theorem, Konig's theorem. Coloring maps. 6. Maximum flow problems (2 timeslots) Ford-Fulkerson's algorithm. 7. Matching (2 timeslots) Matchings, in particular, bipartite matchings. Hall's theorem, Hungarian method. 8. Exam (1 timeslot)
Evaluation Methods and Policy	Mainly evaluated by the final exam. In some cases, exercises or the number of attendance to the class may be considered.
Course Requirements	Basics of algorithms, data structures, and set theory.
Study outside of Class (preparation and review)	Reading the textbook is effective for study. Due to time constraints, I do not give complete description of the proofs in class. I strongly recommend do it by yourself after the class.
Textbooks	Textbooks/References	グラフ理論入門 ～基本とアルゴリズム～, 宮崎修一, (森北出版株式会社), ISBN:978-4-627-85281-5, Written in Japanese
References, etc.	I may show some recommended books in class.
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