{"id":156443,"date":"1996-01-01T00:00:00","date_gmt":"1996-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/on-the-number-of-edges-in-cycletrees\/"},"modified":"2018-10-16T20:23:02","modified_gmt":"2018-10-17T03:23:02","slug":"on-the-number-of-edges-in-cycletrees","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/on-the-number-of-edges-in-cycletrees\/","title":{"rendered":"On the number of edges in cycletrees"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Given N vertices v1,\u2026, vn, how many edges does it take to form a graph that contains a Hamiltonian cycle (v1, v2,\u2026, vN, v1) and a basic binary spanning tree with some vertex vr as root? In this article the question is answered exactly. Moreover, it is shown that for any odd N there exists a natural cycletree with N vertices, a minimal number of edges and a minimal total path length.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given N vertices v1,\u2026, vn, how many edges does it take to form a graph that contains a Hamiltonian cycle (v1, v2,\u2026, vN, v1) and a basic binary spanning tree with some vertex vr as root? In this article the question is answered exactly. Moreover, it is shown that for any odd N there exists [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13547],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-156443","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-systems-and-networking","msr-locale-en_us"],"msr_publishername":"Elsevier","msr_edition":"Information Processing 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