Handshaking lemma

In graph theory, a branch of mathematics, the handshaking lemma is the statement that every finite undirected graph has an even number of vertices with odd degree (the number of edges touching the vertex).

{\displaystyle \sum _{v\in V}\deg v=2|E|}

- From Wikipedia, the free encyclopedia

Railroad is one of the challenges that can be solved using this lemma.

Solution is if 4X +3Y ≡ 0 mod 2, then possible. Otherwise, it is impossible.

And it can be reduced to just checking whether Y is even or odd.

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