Graph Theory
Combinatorics practice with graphs. The B version of the unit is aimed at students with no previous exposure to graph theory; the harder versions assume prior experience.
Graph Theory unit focuses on an olympiad based approach towards graph theory. Having some familiarity with some graph theory terminologies may help, but not necessary.
It has B, D and Z versions of it.
Personal Opinion --- There are tons of materials available on internet on graph theory, but one should not make an assumption how this handout could be because the approaches toward graph theory are somehow different due to academic preferences. As an example, olympiad based approaches for graph theory are different to an CS undergrad course. This unit focuses heavily on problem solving with graph representation of a combinatorics problem. It involves some algorithmic problems as well.
Should I do this unit?
Yes of course! Graph theoretical problems tends to be quite nice and often invoke a sense of order when you reduced the problem to some structure.
Philosophy
The core philosophy one may learn from this is to see olympiad combinatorics problems with a graph theory view. E.g. ISL 2005 C1 can be solved with other methods but involving graph theory based approach gives a more nicer (easier) solution.
Notable Problems
-
RMM 2020/3 -- Specially recommended. One of the hardest (nicest) problem of this unit.
-
German TST 2004 --- Induction is one of the most powerful weapon for graph theory approach, this problem showcases this idea.
-
EGMO 2017/4 Exceptionally nice (somewhat easy). Spoiler -- Taking a clique could be helpful.