[Merged by Bors] - feat(combinatorics/simple_graph/degree_sum): degree-sum formula and handshake lemma #5263
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Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
Co-authored-by: Bhavik Mehta <bhavikmehta8@gmail.com>
…ity/mathlib into simple_graphs3 grabbing commits from github
Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
…ity/mathlib into simple_graphs3 implementing changes
Co-authored-by: Aaron Anderson <65780815+awainverse@users.noreply.github.com>
…ity/mathlib into simple_graphs3 fdsjka
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
…ity/mathlib into simple_graphs3 pulling new commits
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Yeah I think this new definition to the |
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I think the filename could be a little more general and make contact with the names of its declarations, maybe degree_sum.lean?
I made a few name suggestions; apologies if I missed some of the renamings.
LGTM once the TODO_move section is put in the right spot.
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I'm doing this from my laptop, which doesn't have lean installed, so this might take another commit if I made a mistake.
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…andshake lemma (#5263) Adds the theorem that the sum of the degrees of the vertices of a simple graph is twice the number of edges. Also adds corollaries like the handshake lemma, which is that the number of odd-degree vertices is even. The corollary `exists_ne_odd_degree_if_exists_odd` is in anticipation of Sperner's lemma. Co-authored-by: agusakov <39916842+agusakov@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com>
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Adds the theorem that the sum of the degrees of the vertices of a simple graph is twice the number of edges. Also adds corollaries like the handshake lemma, which is that the number of odd-degree vertices is even.
The corollary
exists_ne_odd_degree_if_exists_oddis in anticipation of Sperner's lemma.