{"id":148,"date":"2023-02-01T00:03:23","date_gmt":"2023-02-01T00:03:23","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/chapter\/assignments-euler-and-hamilitonian-circuits\/"},"modified":"2023-02-01T00:03:23","modified_gmt":"2023-02-01T00:03:23","slug":"assignments-euler-and-hamilitonian-circuits","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/chapter\/assignments-euler-and-hamilitonian-circuits\/","title":{"raw":"Assignment: Euler and Hamiltonian Circuits","rendered":"Assignment: Euler and Hamiltonian Circuits"},"content":{"raw":"\n<ol>\n \t<li>You and your friends want to tour the southwest by car. You will visit the nine states below, with the following rather odd rule: you must cross each border between neighboring states exactly once (so, for example, you must cross the Colorado-Utah border exactly once). Can you do it? If so, does it matter where you start your road trip? What fact about graph theory solves this problem?\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/17171703\/Screen-Shot-2017-03-17-at-10.16.46-AM.png\"><img class=\" wp-image-1901 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/17171703\/Screen-Shot-2017-03-17-at-10.16.46-AM.png\" alt=\"Map of the US with the following states shaded: California, Arizona, New Mexico, Texas, Oklahoma, Nebraska, Colorado, Utah, Nevada. Each of the states shares a border with another of the states listed.\" width=\"435\" height=\"320\"><\/a><\/li>\n \t<li>Below is a graph representing friendships between a group of students (each vertex is a student and each edge is a friendship). Is it possible for the students to sit around a round table in such a way that every student sits between two friends? What does this question have to do with paths?<\/li>\n<\/ol>\n&nbsp;\n\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/17172022\/Screen-Shot-2017-03-17-at-10.19.40-AM.png\"><img class=\" wp-image-1902 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/17172022\/Screen-Shot-2017-03-17-at-10.19.40-AM.png\" alt=\"\" width=\"377\" height=\"363\"><\/a>\n\n&nbsp;\n","rendered":"<ol>\n<li>You and your friends want to tour the southwest by car. You will visit the nine states below, with the following rather odd rule: you must cross each border between neighboring states exactly once (so, for example, you must cross the Colorado-Utah border exactly once). Can you do it? If so, does it matter where you start your road trip? What fact about graph theory solves this problem?<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/17171703\/Screen-Shot-2017-03-17-at-10.16.46-AM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1901 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/17171703\/Screen-Shot-2017-03-17-at-10.16.46-AM.png\" alt=\"Map of the US with the following states shaded: California, Arizona, New Mexico, Texas, Oklahoma, Nebraska, Colorado, Utah, Nevada. Each of the states shares a border with another of the states listed.\" width=\"435\" height=\"320\" \/><\/a><\/li>\n<li>Below is a graph representing friendships between a group of students (each vertex is a student and each edge is a friendship). Is it possible for the students to sit around a round table in such a way that every student sits between two friends? What does this question have to do with paths?<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/17172022\/Screen-Shot-2017-03-17-at-10.19.40-AM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1902 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/17172022\/Screen-Shot-2017-03-17-at-10.19.40-AM.png\" alt=\"\" width=\"377\" height=\"363\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"author":538461,"menu_order":29,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-148","chapter","type-chapter","status-publish","hentry"],"part":119,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/148","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/users\/538461"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/148\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/parts\/119"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapters\/148\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/media?parent=148"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=148"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/contributor?post=148"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ct-state-quantitative-reasoning\/wp-json\/wp\/v2\/license?post=148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}