{"id":14799,"date":"2022-05-28T20:20:52","date_gmt":"2022-05-29T00:20:52","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=14799"},"modified":"2026-06-09T10:52:48","modified_gmt":"2026-06-09T14:52:48","slug":"tr-175-separation-of-graphs-of-bounded-genus","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1990\/tr-175-separation-of-graphs-of-bounded-genus\/","title":{"rendered":"TR-175: Separation of Graphs of Bounded Genus"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-175: Separation of Graphs of Bounded Genus\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n\n\n<p>Carleton University<br><a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1990\/\">Technical Report<\/a>&nbsp;<strong>TR-175<\/strong><br>May 1990<\/p>\n\n\n\n<h2 id=\"separation-of-graphs-of-bounded-genus\" class=\"wp-block-heading\">Separation of Graphs of Bounded Genus<\/h2>\n\n\n\n<p>Ljudmil G. Aleksandrov &amp; Hristo N. Djidjev<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>In this paper we improve some separator theorems for graphs of bounded genus. Let G be an n vertex connected graph of orientable genus g and T be a spanning tree of G. Any simple cycle of G that contains exactly one edge not in T is called a T-cycle of G. First we show that, if G is a triangulation, there exist g+l T-cycles of G whose removal divides G into components of no more than (2\/3 )n vertices each. This improves the best previous 2g+l bound. The tool used to obtain this result is a sparse weighted graph associated with the genus g imbedding of G. Next we prove that a set C called a separator<br>of no more than \u2713 (6g+6)n vertices of G that divides G. into components of no more than (2\/3 )n vertices each exists. This is an improvement over the best previous \u2713 ( 12g +6 )n bound on the size of C. Similar results are derived for graphs imbedded on non-orientable surfaces. A lower bound on the size of the smallest separator for toroidal graphs is obtained.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-175.pdf\">TR-175.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report&nbsp;TR-175May 1990 Separation of Graphs of Bounded Genus Ljudmil G. Aleksandrov &amp; Hristo N. Djidjev Abstract In this paper we improve some separator theorems for graphs of bounded genus. Let G be an n vertex connected graph of orientable genus g and T be a spanning tree of G. Any simple cycle of [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11906,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_cu_dining_location_slug":"","footnotes":"","_links_to":"","_links_to_target":""},"cu_page_type":[],"class_list":["post-14799","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14799","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=14799"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14799\/revisions"}],"predecessor-version":[{"id":24538,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14799\/revisions\/24538"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11906"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=14799"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=14799"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}