Basic graph theory matching question -- I don't understand the answer to this We generalize the idea of matching in Example 1 to arbitrary graphs by defining
a matching to be a pairing off of adjacent vertices in a graph. For example, one
possible matching in Figure 1.1 is a-b, c-d. For Figure 1.2, is there matching?  If not, explain why.
Figure 1.1 

Figure 1.2

The answer in the book says this:
a,c,e collectively must be matched with just b and e.
I am assuming the answer means no, there is no match.  But, the answer doesn't make sense to me.  If a match is a pairing off of adjacent vertices, then a-b and d-e must be adjacent vertices in some pair.  I'm not sure if vertices can be used again in a match, but if not, then vertex c makes it impossible for either a-b or d-e to be used in a match with c.  I'm not sure what to make of the answer or question.  I'm trying to find a solutions manual, but no luck.
Any thoughts?
 A: Presumably the book has a typo and it should say $a$, $c$, and $e$ must be matched with $b$ and $d$.
Your logic is correct and emulates what the book is trying to say which is that there can be no perfect matching (I'll define this in a second) because it is impossible to find a match for $c$ since $b$ and $d$ are already taken by $a$ and $e$ respectively.
A matching cannot reuse vertices.
Now, your book is a little bit misleading in that it seems to be using the term 'matching' to refer to a 'perfect matching'. A matching is properly defined as set of edges without common vertices, while a perfect matching is a matching such that every vertex in the graph is adjacent to some edge in the matching. 
In the second example, a valid matching would be $\{(b,h),(c,d)\}$ where $(x,y)$ refers to the edge between vertices $x$ and $y$. The empty set would even be a valid matching. So in answer to the question, there certainly exist matchings in the the second example, but there are not any perfect matchings.
To learn more, see the Wikipedia page on matching.
