{"id":4970,"date":"2023-12-15T12:36:56","date_gmt":"2023-12-15T11:36:56","guid":{"rendered":"https:\/\/erlebnisland-mathematik.de\/?page_id=4970"},"modified":"2024-01-03T13:35:26","modified_gmt":"2024-01-03T12:35:26","slug":"advanced-text-round-trips-through-saxony","status":"publish","type":"page","link":"https:\/\/erlebnisland-mathematik.de\/en\/advanced-text-round-trips-through-saxony\/","title":{"rendered":"Round trips through Saxony"},"content":{"rendered":"

[vc_row drowwidth=”sidebar-biest-default sidebar-biest”][vc_column][vc_column_text]<\/p>\n

Round trips through Saxony<\/h1>\n

Imagine you are planning a round trip through the largest cities in Saxony. You only want to visit each city once and the round trip should be as short as possible. The “Round trip through Saxony” exhibit allows you to plan your journey as efficiently as possible.<\/p>\n

[\/vc_column_text][vc_single_image image=”4933″ img_size=”large” alignment=”center”]Figure 1: The exhibit[\/vc_single_image][vc_column_text]<\/p>\n

And now … the mathematics:<\/h3>\n

[\/vc_column_text][vc_column_text]Such a problem is also called the “<\/a>Traveling Salesmen Problem<\/a>“<\/a><\/em> (TSP).<\/em> This can be modeled using graphs<\/a>. An (undirected) graph is an entity that consists of vertices and edges. Each edge connects two vertices (cf. [1]). For example, the “House of St Nicholas” is a graph consisting of 5 corners and 8 edges (see also the exhibit “Euler’s lines”<\/a>).[\/vc_column_text][vc_single_image image=”4945″ img_size=”medium” alignment=”center”]Abbildung 2: House of St Nicholas[\/vc_single_image][vc_column_text]<\/p>\n

\u00a0In mathematics, we write this as follows: A graph \"(V,E)\" consists of<\/div>\n