Course details

Graph Algorithms

GAL Acad. year 2016/2017 Winter semester 5 credits

Current academic year

This course discusses graph representations and graphs algorithms for searching (depth-first search, breadth-first search), topological sorting, graph components and strongly connected components, trees and minimal spanning trees, single-source and all-pairs shortest paths, maximal flows and minimal cuts, maximal bipartite matching, Euler graphs, and graph coloring. The principles and complexities of all presented algorithms are discussed.


Language of instruction



Examination (written)

Time span

39 hrs lectures, 13 hrs projects

Assessment points

60 exam, 15 half-term test, 25 projects




Křivka Zbyněk, Ing., Ph.D. (DIFS FIT BUT)
Soukup Ondřej, Ing. (DIFS FIT BUT)

Subject specific learning outcomes and competences

Fundamental ability to construct an algorithm for a graph problem and to analyze its time and space complexity.

Learning objectives

Familiarity with graphs and graph algorithms with their complexities.

Prerequisite kwnowledge and skills

Foundations in discrete mathematics and algorithmic thinking.

Study literature

  • Copy of lectures.
  • T.H. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms, McGraw-Hill, 2002.

Fundamental literature

  • T.H. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms, McGraw-Hill, 2002.
  • J. Demel, Grafy, SNTL Praha, 1988.
  • J. Demel, Grafy a jejich aplikace, Academia, 2002. (More about the book)
  • R. Diestel, Graph Theory, Third Edition, Springer-Verlag, Heidelberg, 2000.
  • J.A. McHugh, Algorithmic Graph Theory, Prentice-Hall, 1990.
  • J.A. Bondy, U.S.R. Murty: Graph Theory, Graduate text in mathematics, Springer, 2008.
  • J.L. Gross, J. Yellen: Graph Theory and Its Applications, Second Edition, Chapman & Hall/CRC, 2005.
  • J.L. Gross, J. Yellen: Handbook of Graph Theory (Discrete Mathematics and Its Applications), CRC Press, 2003.

Syllabus of lectures

  1. Introduction, algorithmic complexity, basic notions and graph representations.
  2. Graph searching, depth-first search, breadth-first search.
  3. Topological sort, acyclic graphs.
  4. Graph components, strongly connected components, examples.
  5. Trees, minimal spanning trees, algorithms of Jarník and Borůvka.
  6. Growing a minimal spanning tree, algorithms of Kruskal and Prim.
  7. Single-source shortest paths, the Bellman-Ford algorithm, shortest path in DAGs.
  8. Dijkstra's algorithm. All-pairs shortest paths.
  9. Shortest paths and matrix multiplication, the Floyd-Warshall algorithm.
  10. Flows and cuts in networks, maximal flow, minimal cut, the Ford-Fulkerson algorithm.
  11. Matching in bipartite graphs, maximal matching.
  12. Euler graphs and tours and Hamilton cycles.
  13. Graph coloring.

Syllabus - others, projects and individual work of students

  1. Solving of selected graph problems and presentation of solutions (principle, complexity, implementation, optimization).

Progress assessment

A mid-term exam evaluation (max. 15 points) and an evaluation of projects (max. 25 points).

Controlled instruction

A written mid-term exam, an evaluation of projects, and a final exam. The minimal number of points which can be obtained from the final exam is 25. Otherwise, no points will be assigned to a student.

Course inclusion in study plans

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