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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.
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Linear independence of vectors in Graph Theory
I have poste this question on StackExchange but there were no takers - would I be luckier on this site?
Most of this is well known, so let me just restate the corresponding Math:
Given a connected, di …
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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 …
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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 …