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<div>Tournament graphs are used in discrete mathematics to represent a winning vertex in a graph. A tournament is a complete graph in which every pair of vertices are connected by a directed edge. These types of graphs are referred to as tournaments because each of the <span class="ltx_Math" contenteditable="false" data-equation="n">\(n\)</span> players competes against the other <span class="ltx_Math" contenteditable="false" data-equation="n-1">\(n-1\)</span> players where ties are not allowed and the winner can be represented on a graph. These graphs are created by assigning every player a vertex and if player <span class="ltx_Math" contenteditable="false" data-equation="1">\(1\)</span> beats player <span class="ltx_Math" contenteditable="false" data-equation="2">\(2\)</span>, then a directed edge can be drawn with the arrow pointing from <span class="ltx_Math" contenteditable="false" data-equation="1">\(1\)</span> to <span class="ltx_Math" contenteditable="false" data-equation="2.">\(2.\)</span> Tournaments graphs create Hamiltonian paths that go through each vertex. The Hamiltonian path theorem states that for every tournament there is a Hamiltonian path for <span class="ltx_Math" contenteditable="false" data-equation="n\ge1,">\(n\ge1,\)</span> for any tournament consisting of <span class="ltx_Math" contenteditable="false" data-equation="n">\(n\)</span> vertices in which there is always a sequence of vertices <span class="ltx_Math" contenteditable="false" data-equation="v_1,v_2,...,v_n">\(v_1,v_2,...,v_n\)</span> such that <span class="ltx_Math" contenteditable="false" data-equation="v_1\rightarrow v_2\rightarrow...\rightarrow v_n.">\(v_1\rightarrow v_2\rightarrow...\rightarrow v_n.\)</span><br></div>
