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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 votes
2 answers
599 views

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 …
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