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最近得到一本好书,书名是<Graph Theory:1736-1936> by N.L. Biggs, E.K. Lloyd, R.J. Wilson。先把目录抄下来,与有兴趣的朋友分享。以后,读完每一章,争取写些评论和体会。这对于一个医学背景的人,也是需要一定的努力的。
试试吧,毕竟这才是自己的兴趣所在。
(contents)
1. PATHS
The problem of the konigsberg bridges
Diagram-tracing puzzles
Mazes and labyrinths
2. CIRCUITS
The knight's tour
Kirkman and polyhedra
The Icosian Game
3. TREES
The first studies of trees
Counting unrooted trees
Counting labelled trees
4. CHEMICAL GRAPHS
Graphic formulae in chemistry
Isomerism
Clifford, Sylvester, and the term "graph"
Enumeration, from Cayley to Polya
5. EULER'S POLYHEDRAL FORMULA
The history of polyhedra
Planar graphs and maps
Generalizations of Euler's formulae
6. THE FOUR-COLOUR PROBLEM-ERALY HISTORY
The origin of the four-colour problem
The "proof"
Heawood and the five-colour theorem
7. COLOURING MAPS ON SURFACES
The chromatic number of a surface
Neighbouring regions
One-sided surfaces
8. IDEAS FROM ALGEBRA AND TOPOLOGY
The algebra of circuits
Planar graphs
Planarity and Whitney duality
9. THE FOUR-COLOUR PROBLEM- TO 1936
The first attempts to reformulate the problem
Reducibility
Birkhoff, Whitney, and chromatic polynomials
10. THE FACTORIZATION OF GRAPHS
Regular graphs and their factors
Petersen's theorem on trivalent graphs
An alternative view: correspondences
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