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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 ]
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 ...
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 ...
Republic of Philippines v. Pimentel , [ note 1 ] 553 U.S. 851 (2008), is a decision of the Supreme Court of the United States which clarified the Federal Rules of Civil Procedure as regards money damages sought by a foreign government, the Republic of the Philippines , via its Presidential Commission on Good Government (PCGG).
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.
The Huffington Post spoke with psychology professors about what this may mean. Florin Dolcos, a University of Illinois associate psychology professor and faculty member at the Beckman Institute's ...
The terms legal case management (LCM), legal management system (LMS), matter management or legal project management refer to a subset of law practice management and cover a range of approaches and technologies used by law firms and courts to leverage knowledge and methodologies for managing the life cycle of a case or matter more effectively.
By Kathleen Elkins and Skye Gould In Brazil and the United States, a firm handshake is expected. This would be off putting in the UK, as the British like to greet each other with a lighter handshake.