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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.
4
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answers
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Co-trees of a simple graph
Consider fundamental cycles (say $k$ of them) of a specific spanning tree of a simple graph (with $m$ edges) which is also connected and has no one-edge bonds.
Make the graph directed (in an arbitrary …
1
vote
Co-trees of a simple graph
Consider 2 different spanning trees of the graph, and the corresponding cotrees and fundamental cycles. Then $$C_2=C_2|S_1*C_1$$ spells out the algebraic details of the following well-known fact: ever …