The tutor considers a problem from Grimaldi about max trail length on Kn. For a briefing about the complete graph Kn, check my post from yesterday. In graph theory, a trail is a route that doesn’t repeat any edges. Unlike …

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The tutor introduces the idea of the complete graph. The complete graph on n vertices, Kn, means the graph in which each vertex is connected to each other one. When two vertices are connected by an edge, they can be …

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The tutor proves the existence of a Hamilton cycle under certain conditions. A Hamilton cycle, named for the Irish mathematician Sir William Rowan Hamilton, is a path that visits each vertex of a graph exactly once before returning to the …

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The tutor shows the easy concept, from graph theory, of elementary subdivision. An elementary subdivision on a graph replaces one edge by two, with a new vertex installed between them. Consider the following two graphs: Graph 1 Graph 2 Graph …

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