Editing Combinatorics (section)

===Graph theory===
[[Image:Petersen1 tiny.svg|thumb|150px|[[Petersen graph]].]]
{{Main|Graph theory}}

Graphs are fundamental objects  in combinatorics.  Considerations of graph theory range from enumeration (e.g., the number of graphs on ''n'' vertices with ''k'' edges) to existing structures (e.g., Hamiltonian cycles) to algebraic representations (e.g., given a graph ''G'' and two numbers ''x'' and ''y'', does the [[Tutte polynomial]] ''T''<sub>''G''</sub>(''x'',''y'') have a combinatorial interpretation?).  Although there are very strong connections between graph theory and combinatorics, they are sometimes thought of as separate subjects.<ref>Sanders, Daniel P.; [http://www.math.gatech.edu/~sanders/graphtheory/writings/2-digit.html ''2-Digit MSC Comparison''] {{webarchive|url=https://web.archive.org/web/20081231163112/http://www.math.gatech.edu/~sanders/graphtheory/writings/2-digit.html |date=2008-12-31 }}</ref>  While combinatorial methods apply to many graph theory problems, the two disciplines are generally used to seek solutions to different types of problems.