Osion kuvaus

  • Graphs are widely used as modelling devices in scheduling, networking, material physics and many other sciences, and even to model other purely mathematical objects such as knots, groups and manifolds. In this course, our focus will be on the combinatorial theory of graphs, with views towards its rich interplay with algebra, computer science and probability theory.

    The course is aimed at master's and doctoral students, so mathematical maturity comparable to a bachelor in computer science, mathematics or operations research is expected.

    The course will be graded based on three homework sets, each containing 7 "exercises" and 3 "problems". We reserve the right to require an oral exam in addition, if we are not sure about the grade based on the homework.

    Welcome!

    Teachers: Ragnar Freij-Hollanti and Matteo Allaix

    Lectures: Mon 10-12 and Wed 12-14.
    Excercises: Fri 12-14.

    All events start 15 past the hour at the address https://aalto.zoom.us/j/67316483735

    We have also a Zulip organization in order to ask questions about lectures and exercises, here is the address in order to join: https://ms-e1050-gt-course.zulipchat.com/join/eb32sdarhaxf6tcvr2xxd52q/

    Make sure to connect and test your technology in advance of the start of the lecture.


    Lecture schedule (with references to chapters in Diestel's book):
    1) Basics (1.1-4)
    2) Basics (1.5-7,9)
    3) Menger's Theorem and matchings (3.3, 2.1)
    4) Matchings and plane graphs (2.1,2, 4.2)
    5) 3-connected and planar graphs (3.2, 4.3,4,6)
    6) Colorings (5.1-4)
    7) Perfect graphs (5.5)
    8) Extremal graph theory (7.1-3)
    9) Szemeredi’s Regularity Lemma (7.4-5)
    10) Ramsey theory (9.1-2)
    11) Chromatic polynomial and flow polynomial
    12) The Tutte polynomial