{"id":14924,"date":"2022-06-13T17:31:22","date_gmt":"2022-06-13T21:31:22","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=14924"},"modified":"2022-06-13T17:31:49","modified_gmt":"2022-06-13T21:31:49","slug":"tr-186-reduced-constants-for-simple-cycle-graph-separation","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/","title":{"rendered":"TR-186: Reduced Constants for Simple Cycle Graph Separation"},"content":{"rendered":"

Carleton University
\nTechnical Report<\/a> TR-186<\/strong>
\nFebruary 1991<\/p>\n

Reduced Constants for Simple Cycle Graph Separation<\/h2>\n
\n
Hristo N. Djidjev & Shankar M. Venkatesan<\/div>\n<\/div>\n
\n

Abstract<\/h3>\n

If G is an n vertex maximal planar graph, then the vertex set of G can be partitioned into three sets A, B, C such that neither A nor 8 contains more than (1-B)n vertices for any B:::;1 \/3, no edge from G connects a vertex in A to a vertex in 8, and C is a cycle in G containing no more than (\u2713 2B+\u2713 2-2B)\u2713n+0(1) vertices. Specifically, when B=1\/3, the separator C is of size (\u2713 2\/3+\u2713 4\/3)”n+0(1 ), which is roughly 1.971197\u2713n. The constant 1.971197 is an improvement over the best known so far result of Miller 2\u2713 2 = 2.828427. If non\u00adnegative weights adding to at most 1 are associated with the vertices of G, then the vertex set of G can be partitioned into three sets A, 8, C such that neither A nor B has weight exceeding 1-B, no edge from G connects a vertex in A to a vertex in 8, and C is a simple cycle with no more than 2\u2713n+0(1) vertices.<\/p>\n<\/div>\n

TR-186.pdf<\/a><\/p>\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Carleton University Technical Report TR-186 February 1991 Reduced Constants for Simple Cycle Graph Separation Hristo N. Djidjev & Shankar M. Venkatesan Abstract If G is an n vertex maximal planar graph, then the vertex set of G can be partitioned into three sets A, B, C such that neither A nor 8 contains more than […]<\/p>\n","protected":false},"author":49,"featured_media":0,"parent":11908,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":"","_links_to":"","_links_to_target":""},"yoast_head":"\nTR-186: Reduced Constants for Simple Cycle Graph Separation - School of Computer Science<\/title>\n<meta name=\"description\" content=\"Carleton University Technical Report TR-186 February 1991 Reduced Constants for Simple Cycle Graph Separation Hristo N. Djidjev & Shankar M.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/\",\"url\":\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/\",\"name\":\"TR-186: Reduced Constants for Simple Cycle Graph Separation - School of Computer Science\",\"isPartOf\":{\"@id\":\"https:\/\/carleton.ca\/scs\/#website\"},\"datePublished\":\"2022-06-13T21:31:22+00:00\",\"dateModified\":\"2022-06-13T21:31:49+00:00\",\"description\":\"Carleton University Technical Report TR-186 February 1991 Reduced Constants for Simple Cycle Graph Separation Hristo N. Djidjev & Shankar M.\",\"breadcrumb\":{\"@id\":\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/carleton.ca\/scs\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Research\",\"item\":\"https:\/\/carleton.ca\/scs\/research\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"SCS Technical Reports\",\"item\":\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Technical Reports 1991\",\"item\":\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/\"},{\"@type\":\"ListItem\",\"position\":5,\"name\":\"TR-186: Reduced Constants for Simple Cycle Graph Separation\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/carleton.ca\/scs\/#website\",\"url\":\"https:\/\/carleton.ca\/scs\/\",\"name\":\"School of Computer Science\",\"description\":\"Carleton University\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/carleton.ca\/scs\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"TR-186: Reduced Constants for Simple Cycle Graph Separation - School of Computer Science","description":"Carleton University Technical Report TR-186 February 1991 Reduced Constants for Simple Cycle Graph Separation Hristo N. Djidjev & Shankar M.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/","url":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/","name":"TR-186: Reduced Constants for Simple Cycle Graph Separation - School of Computer Science","isPartOf":{"@id":"https:\/\/carleton.ca\/scs\/#website"},"datePublished":"2022-06-13T21:31:22+00:00","dateModified":"2022-06-13T21:31:49+00:00","description":"Carleton University Technical Report TR-186 February 1991 Reduced Constants for Simple Cycle Graph Separation Hristo N. Djidjev & Shankar M.","breadcrumb":{"@id":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-186-reduced-constants-for-simple-cycle-graph-separation\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/carleton.ca\/scs\/"},{"@type":"ListItem","position":2,"name":"Research","item":"https:\/\/carleton.ca\/scs\/research\/"},{"@type":"ListItem","position":3,"name":"SCS Technical Reports","item":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/"},{"@type":"ListItem","position":4,"name":"Technical Reports 1991","item":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/"},{"@type":"ListItem","position":5,"name":"TR-186: Reduced Constants for Simple Cycle Graph Separation"}]},{"@type":"WebSite","@id":"https:\/\/carleton.ca\/scs\/#website","url":"https:\/\/carleton.ca\/scs\/","name":"School of Computer Science","description":"Carleton University","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/carleton.ca\/scs\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"}]}},"acf":{"banner_button":"no","banner_image_type":"none"},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14924"}],"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\/49"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=14924"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14924\/revisions"}],"predecessor-version":[{"id":14926,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14924\/revisions\/14926"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11908"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=14924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}