Additional Problems
(1) Is K5 planar? What about K5 − e where e is an arbitrary edge?
(2) Find an infinite family of non-planar graphs.
(3) Convince yourself and your friends that you know how to prove
the “handshaking theorem” for connected planar graphs, i.e.,
that
X
2|E| =
deg(f ).
f ∈F
(4) Make sure you understand the proof that a connected planar
graph with at least three vertices must satisfy |E| ≤ 3|V | − 6.
(5) Let H be a subgraph of G. Is there a relation between χ(H)
and χ(G)?
(6) Look up the proof that there are only five platonic solids. Use
your graph-theoretic knowledge to understand it.
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