Graph Theory

Numbering Code U-ENG29 29030 LJ10 Year/Term 2022 ・ First semester
Number of Credits 2 Course Type Lecture
Target Year Target Student
Language Japanese Day/Period Thu.2
Instructor name NAGAMOCHI HIROSHI (Graduate School of Informatics Professor)
Outline and Purpose of the Course After basic notations and properties on graphs and networks are given, algorithms to some representative problems such as the shortest path problem, the minimum spanning tree problem and the maximum flow problem are described. Applications of these results and extensions of them in discrete mathematics are also presented.
Course Goals Not only to learn the notions on graph structure as knowledge but to understand proofs to mathematical properties on discrete structures and logical mechanisms in computational methods
Schedule and Contents graphs and networks ,1time,Basic terminology on graphs and networks are defined, and some representative problems such as the Eulerian trail problem, the Hamiltonian cycle problem and the graph isomorphism problem are introduced.
connectivity,1time,Graph connectivity such as k-connectivity of undirected graphs and strong connectivity of digraphs are defined and some properties for them are derived.
plane graphs and dual graphs,2times,Some combinatorial aspects of graphs such as Kratowski's theorem, which characterizes the planar graphs, duality of plane graphs, the four-color theorem are described.
representation for graphs,1time,As representation for data to input graphs, matrix and adjacency lists are introduced.
graph search,2times,The depth first search and the width first search are introduced, and as their applications, an algorithm for computing cut-vertices and biconnected components is designed.
shortest path ,2times,Properties on shortest paths and Dijkstra's method, as a representative shortest path algorithm, are described.
trees and cut-sets,1time,Important properties on spanning trees and cut-sets, especially the roles of fundamental cycles and fundamental cut-sets are described.
minimum spanning tree ,1-2times,Kruskal's method and Prim's method, as representative minimum spanning tree algorithms, are described, and data structure for them and their computational complexities are discussed.
maximum-flow ,2times,The maximum-flow and minimum-cut theorem in networks and an algorithm for finding a maximum flow are described.
Evaluation Methods and Policy Evaluation is made based on marks on answers in exercises (30%) and score of end-term examination (70%)
Course Requirements None
References, etc. C ni yoru Algorithms to Data Structure, Ibaraki, Shokou-do isbn{}{4785631171} isbn{}{9784274216046}
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