Graphs: Difference between revisions
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Revision as of 01:55, 19 August 2017
Graphs are mathematical objects consisting of nodes and edges. The original inventor of graph theory was Leonhard Euler, who used it to solve the Seven Bridges of Königsberg problem.
Notes
Diestel - Graph Theory
Link to book: http://www.cs.unibo.it/babaoglu/courses/cas00-01/tutorials/GraphTheory.pdf
Chapter 1: Basics
Chapter 1 is a litany of definitions, concepts, and theorems important to laying the groundwork for discussing graph theory.
Chapter 2: Matching
Bipartite graph matching
k-partite graph matching
Chapter 3: Connectivity
2-connected graphs
3-connected graphs
Menger's Theorem
Mader's Theorem
Spanning trees (and edge-disjoint spanning trees)
Chapter 4: Planar Graphs
Topology
Plane graphs
Algebraic criteria
Chapter 5: Coloring
Coloring vertices
Coloring edges
Chapter 6: Flows
Circulations
Flows in networks
k-flows
Flow coloring
Tutte's flow conjectures
Chapter 7 and 8: Substructures
Subgraphs
Regularity lemma
Hadwigen's theorem
Chapter 9: Ramsey Theory
Chapter 10: Hamilton Cycles
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