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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

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Counting Non-Isomorphic Connected Spanning Graphs on n vertices, m edges

There have been many questions on this site about counting non-isormorphic graphs that are (1) strongly regular, (2) have a certain chromatic number, (3) connected, among many others. What work has b …
Ryan Dougherty's user avatar
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Necessary Conditions for a Graph not possible to Rainbow Color?

Suppose we have a $t$-uniform hypergraph ($t \ge 3$) $G$, and have $t$ colors available. A question in my research is equivalent to asking what the necessary and sufficient conditions are on $G$ for w …
Ryan Dougherty's user avatar