21-301A Combinatorics
Weeks 8,10,11
Trees
Recall that graph is connected, if for any two vertices x, y, the graph always has a path
from x to y.
Denition. A graph T = (V, E) is a tree, if it is connected and contains NO cycle.
For example, a path is a t
21-301 Combinatorics
Oleg Pikhurko
Course Homepage
http:/www.math.cmu.edu/~pikhurko/301/
Instructor
Oleg Pikhurko (Oce: Wean Hall 7105)
Oce Hours: Mon 14:0015:00, Wen 13:0514:00 and Thurs 13:3015:30 on all class days
for the university.
Normally, I will n
21-301A Combinatorics
Weeks 12-13
Partially ordered set
Let X be a nite set.
Denition. R is called a relation on set X, if R X X.
Here X X := cfw_all ordered pairs (x, y) : x, y X denotes the Cartesian product.
If (x, y) R, then we will write it as xRy.