图论教程(英文影印版)

.iii connectivity
3.0 introduction
3.1 vertex cuts and edge cuts
3.2 connectivity and edge-connectivity
3.3 blocks
3.4 cyclical edge-connectivity of a graph
3.5 menger's theorem
3.6 exercises
notes
iv trees
4.0 introduction
4.1 definition, characterization, and simple properties
4.2 centers and centroids
4.3 counting the number of spanning trees
4.4 cayley's formula
4.5 helly property
4.6 exercises
notes
v independent sets and matchings
5.0 introduction
5.1 vertex independent sets and vertex coverings
5.2 edge-independent sets
5.3 matchings and factors
5.4 matchings in bipartite graphs
5.5* perfect matchings and the tutte matrix
notes
vi eulerian and hamiltonian graphs
6.0 introduction
6.1 eulerian graphs
6.2 hamiltonian graphs
6.3* pancyclic graphs
6.4 hamilton cycles in line graphs
6.5 2-factorable graphs
6.6 exercises
notes
vii graph colorings
7.0 introduction
7.1 vertex colorings
7.2 critical graphs
7.3 triangle-free graphs
7.4 edge colorings of graphs
7.5 snarks
7.6 kirkman's schoolgirls problem
7.7 chromatic polynomials
notes
viii p!anarity
8.0 introduction
8.1 planar and nonplanar graphs
8.2 euler formula and its consequences
8.3 k5 and k3.3 are nonplanar graphs
8.4 dual of a plane graph
8.5 the four-color theorem and the heawood five-color theorem
8.6 kuratowski's theorem
8.7 hamiltonian plane graphs
8.8 tait coloring.
notes
ix triangulated graphs
9.0 introduction
9.1 perfect graphs
9.2 triangulated graphs
9.3 interval graphs
9.4 bipartite graph b(g) of a graph g
9.5 circular arc graphs
9.6 exercises
9.7 phasing of traffic lights at a road junction
notes
x applications
10.0 introduction
10.1 the connector problem
10.2 kruskal's algorithm
10.3 prim's algorithm
10.4 shortest-path problems
10.5 timetable problem.
10.6 application to social psychology
10.7 exercises
notes
list of symbols
references
index