There are little exercises-for-the-reader in the beginning of the book, some dating from the Victorian heyday that produced questions one could illustrate; but as the history progresses more of the book is about the people than about the increasingly abstruse problem. It does all wind towards the political or philosophical question that the long, computer-calculated proof produced; to quote Wilson, half the mathematicians at a conference ...could not be convinced that a proof by computer was correct...[half] could not be convinced that...700 pages of hand-calculations could be correct.
Those are not exclusive opinions, grumps the empiric.
Did discrete math look like one body of inquiry before computers? Was it called something else, or did it suffer from the simplicity with which many of its problems can be stated? I wonder only because, on laughably cursory examination, the discrete section in the math library is short and shiny. Maybe the aged classics are in the computer science library. (Not an explanation I often try, that last sentence. I wonder what the oldest book in the CSci library is.)
A Beginner's Guide to Discrete Mathematics, , has nothing explicit about map coloring but, of course, lots of simple graph theory, Hamiltonian cycles, Boolean circuits. Discrete Mathematics: Elementary and Beyond, , , , does mention the four-color theorem (and lots else, including more crypto). The prose in the latter is distractingly perky and humorous, and it's a bit more mathematical and maybe slightly less aimed at CSci than the former. Both provide the puzzles I missed in Wilson.
Shorter versions of the four-colors-suffice proof are already appearing, but that's not where the glory is.
ISBN: 0691115338 (Four Colors Suffice)
ISBN: 0817642692 (A Beginner's Guide...)
ISBN: 0387955852 (Discrete Mathematics:...)