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, ...
First, a preliminary question: Suppose $G$ is a graph with bounded tree-width. If $G$ has a big binary tree minor, prove that $G$ has an induced subgraph which is a subdivision of a large ...
Among the collections of the open problems of Paul Erdős on the website of Professor Fan Chung, there is one called "number of triangle-free graphs". ...