QUESTION 7
The degree sequence of a graph is the list of its vertex degrees written out in increasing order. For example, a two-edge path
has degree sequence 1, 1, 2.
a) (*) Is it true that if $d_1, d_2, \dots, d_n$ is the degree sequence of a graph, then $\sum_i d_i$ is even?
b) (**) Is it true that if $d_1, d_2, \dots, d_n$ is a sequence of integers between zero and n-1 with $\sum_i d_i$ even, then there is an n-vertex
graph with degree sequence $d_1, d_2, \dots, d_n$?
c) (***) Is it true that if $d_1, d_2, \dots, d_n$ is a sequence of integers between one and n-1 with $\sum_i d_i$ even, then there is an n-vertex
graph with degree sequence $d_1, d_2, \dots, d_n$?
