(a) Prove the following claim: in every simple graph G on at
least two vertices, we can always find two distinct vertices v,w
such that deg(v) = deg(w).
(b) Prove the following claim: if G is a simple connected graph
in which the degree of every vertex is even, then we can delete any
edge from G and it will still be connected.
please prove this problem step by step. thanks
Prove that in every simple graph there is a path from every vertex
of odd degree to some other vertex of odd
degree.
Give an example of proof by construction.
For example, prove that for every well-formed formula f in
propositional logic, an equivalent WFF exists in disjunctive normal
form (DNF).
HINT: Every WFF is equivalent to a truth function, and we can
construct an equivalent WFF in full DNF for every truth function.
Explain how.
Prove or disprove: If G = (V; E) is an undirected graph where
every vertex has degree at least 4 and u is in V , then there are
at least 64 distinct paths in G that start at u.