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### Graph algorithm    Record: No

Language: Chinese

Prerequisite

Discrete math.

Abstract

In this course, we introduce basic concepts in graph theory and complexity theory, then study graph algorithms with a focus on matching and network flows.

Reference

1. Introduction to Graph Theory, by Douglas B. West.

2. Modern Graph Theory, by Bela Bollobas.

3. The Design and Analysis of Algorithms, by Dexter Kozen.

Syllabus

(Tentative)

- Foundamental concepts: graphs, paths, walks, cycles, trees, isomorphism, adjacency matrix, complexity classes, reduction, completeness, …

- Matching: bipartite maximum matching, bipartite minimum-cost perfect matching, Primal-dual min-cost matching, online maching…

- Flow: max-flow min-cut theorem, Ford-Fulkerson and Edmonds-Karp algorithms, Dinitz's algorithm, Hopcroft-Karp algorithm, Menger's theorem…

- NP-complete problems: max-cut, independent set, …

- Approximate algorithms: vertex cover, max-cut, graph coloring, …

- Spectural graph theory: Courant-Fischer theorem, graph Laplacian, Cheeger's inequality, graph sparsification, …

Lecturer Intro

Lecturer Email: hanru@bimsa.cn

TA: Dr. Chuqi Cao, chuqicao@bimsa.cn

• ### Graph Theory

Record: YesLevel: GraduateLanguage: EnglishPrerequisiteAbstractThe goal of this course is to give students an overview over the most fundamental concepts and results in modern graph theory.The topics which we plan to cover include: Basic notions: graphs, graph isomorphism, adjacency matrix, paths, cycles, connectivityTrees, spanning trees, Cayley's formula,Vertex and edge connectivity, 2-connec...

• ### Rainbow structures, Latin squares & graph decompositions

Abstract:A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. The study of rainbow subgraphs has a long history in discrete mathematics, going back to the 18th century work of Euler on Latin squares. Since then rainbow structures were the focus of extensive research and found numerous applications in design theory and graph decompositions. Many problem...