Graph Theory 邦迪阅读建议

Optional Topics
Stable Sets and Cliques Stable Sets and Clique Numbers Section12.1
Tur´a n’s Theorem Section12.2
Ramsey Numbers and Ramsey Graphs Section12.3
Bounds on Ramsey Numbers
Vertex Colourings Chromatic Number Section14.1 Matchings Maximum Matchings Section16.1
Matchings in Bipartite Graphs Section16.2 Edge Colourings Edge Chromatic Number Section17.1
Vizing’s Theorem Section17.2 Hamilton Cycles Hamiltonian and Nonhamiltonian Graphs Section18.1
Nonhamiltonian Planar Graphs Section18.2
Path Exchanges Section18.3
Cycle Exchanges
Dirac’s Theorem
Proof Techniques
Inversion Techniques M¨o bius Inversion Section2.7
Inclusion-Exclusion Exercise13.1.3
Exercise14.7.12
Exercise21.2.13 Algebraic Methods Linear Independence Section2.4
Eigenvalues Section3.1
Combinatorial Nullstellensatz Section14.6 Ordering Vertices Bipartite Subgraphs Exercises2.2.2
Exercise2.2.18
Topological Sort Exercise2.5.8
Exercise6.3.9
Median Orders Section4.1
Simplicial Ordering Section9.7
Random Ordering Exercise13.2.10
Exercise13.2.13
Exercise13.3.6
Greedy Heuristics Section14.1
Exercise14.1.9
Exercise14.1.10
Coherent Cyclic Orders Section19.3 Ear Decompositions Section5.3
Directed Ear Decompositions Section5.4 Polynomial Reduction Section8.3
Linear Programming Total Unimodularity Section8.6
Section19.3
F arkas’Lemma Section20.3
Submodularity Balanced Orientations Section9.5
Arc-Disjoint Branchings Section19.4
Packings of Directed Cycles Section19.5
and Directed Bonds
The Regularity Lemma Section12.4 The Probabilistic Method Chapter13
Girth and Chromatic Number Section14.3
Haj´o s’Conjecture Section15.4
Hamilton Cycles Section18.6 Discharging Section15.2
Min-Max Theorems Flows in Networks Chapter7
Linear and Integer Programming Section8.6
Vertex Connectivity Section9.1
Edge Connectivity Section9.3
Perfect Graphs Section14.4
Maximum Matchings Section16.1
Matchings in Bipartite Graphs Section16.2
Matchings in Arbitrary Graphs Section16.3
Perfect Matchings and F actors Section16.4
Coverings and Packings Chapter19
in Directed Graphs
Optional Topics
Flows in Networks Transportation Networks Section7.1
The Max-Flow Min-Cut Theorem Section7.2 Connectivity Vertex Connectivity Section9.1
Edge Connectivity Section9.3
Chordal Graphs Section9.7 Planar Graphs Plane and Planar Graphs Section10.1
F aces Section10.2
Duals
Euler’s Formula Section10.3
Bridges Section10.4
Kuratowski’s Theorem Section10.5 Vertex Colourings Chromatic Number Section14.1 Matchings Maximum Matchings Section16.1
Matchings in Bipartite Graphs Section16.2
Augmenting Path Search Section16.5
Egerv´a ry’s Algorithm
Optional Topics
Complexity of Algorithms Approximation Algorithms Section8.4
Greedy Heuristics Section8.5
Linear and Integer Programming Section8.6 Connectivity Vertex Connectivity Section9.1
Edge Connectivity Section9.3 Planar Graphs Plane and Planar Graphs Section10.1
F aces Section10.2
Duals
Euler’s Formula Section10.3
Bridges Section10.4
Kuratowski’s Theorem Section10.5 Vertex Colourings Chromatic Number Section14.1 Matchings Maximum Matchings Section16.1
Matchings in Bipartite Graphs Section16.2
Augmenting Path Search Section16.5
Egerv´a ry’s Algorithm。