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  2. Handshaking lemma - Wikipedia

    en.wikipedia.org/wiki/Handshaking_lemma

    In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges is even. For example, if there is a party of people who shake hands, the number of people who shake an odd number of other people's hands is even. [ 1 ]

  3. Degree (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Degree_(graph_theory)

    The formula implies that in any undirected graph, the number of vertices with odd degree is even. This statement (as well as the degree sum formula) is known as the handshaking lemma. The latter name comes from a popular mathematical problem, which is to prove that in any group of people, the number of people who have shaken hands with an odd ...

  4. Double counting (proof technique) - Wikipedia

    en.wikipedia.org/wiki/Double_counting_(proof...

    In more colloquial terms, in a party of people some of whom shake hands, an even number of people must have shaken an odd number of other people's hands; for this reason, the result is known as the handshaking lemma. To prove this by double counting, let () be the degree of vertex . The number of vertex-edge incidences in the graph may be ...

  5. Category:Lemmas in graph theory - Wikipedia

    en.wikipedia.org/wiki/Category:Lemmas_in_graph...

    Download QR code; Print/export ... Handshaking lemma; K. KÅ‘nig's lemma; S. Szemerédi regularity lemma This page ...

  6. Template : Did you know nominations/Handshaking lemma

    en.wikipedia.org/.../Handshaking_lemma

    Language links are at the top of the page across from the title.

  7. List of lemmas - Wikipedia

    en.wikipedia.org/wiki/List_of_lemmas

    Burnside's lemma also known as the Cauchy–Frobenius lemma; Frattini's lemma (finite groups) Goursat's lemma; Mautner's lemma (representation theory) Ping-pong lemma (geometric group theory) Schreier's subgroup lemma; Schur's lemma (representation theory) Zassenhaus lemma

  8. Snark (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Snark_(graph_theory)

    By the handshaking lemma, the subgraphs on either side of the bridge have an odd number of vertices each. Whichever of three colors is chosen for the bridge, their odd number of vertices prevents these subgraphs from being covered by cycles that alternate between the other two colors, as would be necessary in a 3-edge-coloring.

  9. Chinese postman problem - Wikipedia

    en.wikipedia.org/wiki/Chinese_postman_problem

    The undirected route inspection problem can be solved in polynomial time by an algorithm based on the concept of a T-join.Let T be a set of vertices in a graph. An edge set J is called a T-join if the collection of vertices that have an odd number of incident edges in J is exactly the set T.