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Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
1
vote
1
answer
43
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Graph classes which have small edge k-cuts
I am interested in graph classes that have the following property: There exists a function $f(k)$ such that for every graph $G$ in the class, for every choice of $k$ vertices $v_1, \ldots, v_k$ in the …
7
votes
1
answer
268
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Is the Rado graph the unique countable graph that has all finite graphs as induced subgraphs?
I understand that since the Rado graph is the Fraïsse limit of the class of finite graphs, it is the unique homogeneous graph with this property. Is there another graph not isomorphic to the Rado grap …