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K-tree
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<p>In <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, a <i>k</i>-tree is an <a href="/facts/Undirected_graph/kw3eIBUe">undirected graph</a> formed by starting with a (<i>k</i> + 1)-vertex <a href="/facts/Complete_graph/AYD6hUqI">complete graph</a> and then repeatedly adding vertices in such a way that each added vertex <i>v</i> has exactly <i>k</i> neighbors <i>U</i> such that, together, the <i>k</i> + 1 vertices formed by <i>v</i> and <i>U</i> form a <a href="/facts/Clique_(graph_theory)/XK9ppLz5">clique</a>. </p>