Basic and Intermediate level knowledge of Graph Theory and Combinatorics. Ability to use induction and other proof techniques within the framework of graphs and Combinatorics
Prerequisites
Linera algebra and
basic group theory
Use of Inductive arguments
Teaching Methods
Presentation of theorems and results in lecture
form followed by class discussion relating to variations and improvements of
the proofs of the statements. Some homework to verify learning
Further information
Attendance contributes about 20% to final grade
Type of Assessment
Four mid-term written examination.
Final oral examination and brief presentation of a theorem by the student
Course program
Depending on the skills and attitude of the students, the course will touch upon easier or more difficult topics.
For each topic, in addition to the basic definitions and theorems, currently open problems will be presented. Home work as well as class work will be devoted to finding proof ideas. The purpose of this approach is to enhance skills to carry on independent research.
Among the various topics the following will be treated:
-- Eigenvalues of graphs
-- The Cauchy-Burnside-Frobenius formula for counting
-- Planar, Eulerian, Hamiltonian graphs
-- Reconstruction of graphs
-- Colorings and Vizing Theorem
-- Kuratowskii Condition of Planarity
-- The Reconstruction Conjecture
-- Intersection of longest paths in connected graphs
== Trees and their characterizations.