MA010 Graph Theory

Fakulta informatiky
podzim 2019
2/1/0. 3 kr. (plus ukončení). Ukončení: zk.
prof. RNDr. Petr Hliněný, Ph.D. (přednášející)
Jacob Cooper, Ph.D. (cvičící)
Robert Arthur Hancock, PhD (cvičící)
RNDr. Deniz Agaoglu Cagirici (pomocník)
Onur Cagirici, M.Sc., Ph.D. (pomocník)
prof. RNDr. Petr Hliněný, Ph.D.
Katedra teorie programování - Fakulta informatiky
Kontaktní osoba: prof. RNDr. Petr Hliněný, Ph.D.
Dodavatelské pracoviště: Katedra teorie programování - Fakulta informatiky
Pá 10:00–11:50 D3
  • Rozvrh seminárních/paralelních skupin:
MA010/01: každé sudé úterý 8:00–9:50 C525, R. Hancock
MA010/02: každé liché úterý 8:00–9:50 C525, R. Hancock
MA010/03: každou sudou středu 14:00–15:50 C525, J. Cooper
MA010/04: každou lichou středu 14:00–15:50 C525, J. Cooper
! PřF:M5140 Teorie grafů &&! NOW ( PřF:M5140 Teorie grafů )
Discrete mathematics, basic concepts of graphs and of graph algorithms. IB000 (or equivalent from other schools) is highly recommended.
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Předmět si smí zapsat nejvýše 200 stud.
Momentální stav registrace a zápisu: zapsáno: 3/200, pouze zareg.: 0/200, pouze zareg. s předností (mateřské obory): 0/200
Mateřské obory/plány
předmět má 26 mateřských oborů, zobrazit
Cíle předmětu
This is a standard course in graph theory, assuming little introductory knowledge of graphs. It aim is to present all usual basic concepts of graph theory, graph properties (with simplified proofs) and formulations of typical graph problems. This is also supplemented with some abstract-level algorithms for the presented problems, and with some advanced graph theory topics. Although the content of this course is primarily targeted at CS students, it is accessible also to others.
Výstupy z učení
At the end of the course, successful students shall understand in depth and tell all the basic terms of graph theory; be able to reproduce the proofs of some fundamental statements on graphs; be able to solve new graph problems; and be ready to apply this knowledge in (especially) computer science applications.
  • Graphs and relations. Subgraphs, isomorphism, degrees. Directed graphs.
  • Graph connectivity and searching, multiple connectivity. Trees, the MST problem.
  • Distance in graphs, graph metrics, concepts of route planning in graphs.
  • Network flows. The "max-flow min-cut" theorem via Ford-Fulkerson's algorithm. Applications to connectivity and representatives.
  • Matching in graphs, packing problems, enumeration.
  • Graph colouring, properties, easy and hard cases. Edge and list colourings.
  • Drawings and planar graphs, duality, Euler's formula and its applications.
  • Computationally hard graph problems on graphs, how to tell "difficulty" of a graph problem.
  • Selected advanced topics (time allowing): Intersection graph representations, chordal graphs, structural width measures, graph minors, graph embeddings on surfaces, crossing number, Ramsey theory.
    povinná literatura
  • DIESTEL, Reinhard. Graph theory. 3rd ed. Berlin: Springer, 2006. xvi, 410s. ISBN 3540261834. info
    doporučená literatura
  • HLINĚNÝ, Petr. Základy teorie grafů. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
  • MATOUŠEK, Jiří a Jaroslav NEŠETŘIL. Kapitoly z diskrétní matematiky. 3., upr. a dopl. vyd. V Praze: Karolinum, 2007. 423 s. ISBN 9788024614113. info
Výukové metody
MA010 is taught in weekly 2-hour lectures, with bi-weekly 2-hour compulsory tutorials. Since this is a mathematical subject, the students are expected to learn the given theory and be able to understand and compose mathematical proofs. Memorizing is not enough! All the study materials, demonstrations, and study agenda are presented through the online IS syllabus.
Metody hodnocení
The resulting grade is taken from a semester test (20%), semester homework assignment (20%), optional bonus work (arbitrary), and a final written exam (60%). The written semester test can be repeated (corrected) once, and the homework assignment can also be rewritten once within the given limits. At least 20% points semester score is strictly required before attending the final exam. Possible bonus points and penalties for not attending the compulsory tutorials count towards this limit. The final written exam for 60% of points consists of a part testing basic graph notions and their applications, and an advanced part in which students have to come with solutions and proofs of rather difficult problems. More then 50% points in total is required to pass.
Vyučovací jazyk
Navazující předměty
Informace učitele
Detailed information regarding course curriculum and examination can be found in the online syllabus MA010 in IS; "**/MA010/index.qwarp".
All students are required to frequently read course news at "".
Since 2016, grading of MA010 changes by including a written homework assignment worth 20% and decreasing the weight of the final exam to 60%.
Since 2009, MA010 is taught in English. Předmět MA010 je od roku 2009 vyučován primárně anglicky. Informace v angličtině mají přednost, české materiály jsou doplňkové.
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Studijní materiály
Předmět je vyučován každoročně.
Nachází se v prerekvizitách jiných předmětů
Předmět je zařazen také v obdobích podzim 2002, podzim 2003, podzim 2004, podzim 2006, podzim 2007, podzim 2008, podzim 2009, podzim 2010, podzim 2011, podzim 2012, podzim 2013, podzim 2014, podzim 2015, podzim 2016, podzim 2017, podzim 2018, podzim 2020, podzim 2021, podzim 2022, podzim 2023.