{"id":16017,"date":"2021-04-01T23:56:47","date_gmt":"2021-04-01T23:56:47","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/chapter\/introduction-euler-paths\/"},"modified":"2021-04-01T23:56:47","modified_gmt":"2021-04-01T23:56:47","slug":"introduction-euler-paths","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/chapter\/introduction-euler-paths\/","title":{"raw":"Introduction to Euler and Hamiltonian Paths and Circuits","rendered":"Introduction to Euler and Hamiltonian Paths and Circuits"},"content":{"raw":"\n<h2>What you\u2019ll learn to do: Find Euler and Hamiltonian paths and circuits within a defined graph<\/h2>\nIn the next lesson, we will investigate specific kinds of paths through a graph called Euler paths and circuits. Euler paths are an optimal path through a graph. They are named after him because it was Euler who first defined them.\n\nBy counting the number of vertices of a graph, and their degree we can determine whether a graph has an Euler path or circuit. We will also learn another algorithm that will allow us to find an Euler circuit once we determine that a graph has one.\n","rendered":"<h2>What you\u2019ll learn to do: Find Euler and Hamiltonian paths and circuits within a defined graph<\/h2>\n<p>In the next lesson, we will investigate specific kinds of paths through a graph called Euler paths and circuits. Euler paths are an optimal path through a graph. They are named after him because it was Euler who first defined them.<\/p>\n<p>By counting the number of vertices of a graph, and their degree we can determine whether a graph has an Euler path or circuit. We will also learn another algorithm that will allow us to find an Euler circuit once we determine that a graph has one.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-16017\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Learning Outcomes and Introduction. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":167848,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Learning Outcomes and Introduction\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"80215870-7383-4d4b-857c-1cd4400fa939","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-16017","chapter","type-chapter","status-publish","hentry"],"part":16012,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/pressbooks\/v2\/chapters\/16017","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/wp\/v2\/users\/167848"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/pressbooks\/v2\/chapters\/16017\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/pressbooks\/v2\/parts\/16012"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/pressbooks\/v2\/chapters\/16017\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/wp\/v2\/media?parent=16017"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/pressbooks\/v2\/chapter-type?post=16017"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/wp\/v2\/contributor?post=16017"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-MGF1107\/wp-json\/wp\/v2\/license?post=16017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}