{"id":12770,"date":"2021-11-20T18:54:53","date_gmt":"2021-11-20T23:54:53","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=12770"},"modified":"2026-06-02T14:59:26","modified_gmt":"2026-06-02T18:59:26","slug":"tr-95-07-stage-graph-representations","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1995\/tr-95-07-stage-graph-representations\/","title":{"rendered":"TR-95-07: Stage-Graph Representations"},"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-95-07: Stage-Graph Representations\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n<p>Carleton University<br>\n<a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1995\/\">Technical Report<\/a> TR-95-07<br>\nMarch&nbsp;1995<\/p>\n\n\n\n<h2 id=\"stage-graph-representations\" class=\"wp-block-heading tr_t1\">Stage-Graph Representations<\/h2>\n\n\n\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">Evangelos Kranakis, Danny Krizanc, Anil Maheshwari, Marc Noy, Jorg-Rudiger Sack, Jorge Urrutia<\/div>\n<\/div>\n<\/div>\n\n\n\n<div>\n<h3>Abstract<\/h3>\n<\/div>\n\n\n\n<p>We consider graph applications of the well-known paradigm &#8220;killing two birds with one stone&#8221;. In the plane, this gives rise to a stage graph as follows: vertices are the points, and {u, v} is an edge if and only if the (in\fnite, straight) line segment joining u to v intersects the stage. Such graphs are shown to be comparability graphs of ordered sets of dimension 2. Similar graphs can be constructed when we have a \fxed number k of stages on the plane. In this case, {u, v} is an edge if and only if the (straight) line segment uv intersects one of the k stages. We study stage representations of stage graphs and give upper and lower bounds on the number of stages needed to represent a graph.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-95-07.pdf\">TR-95-07.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-95-07 March&nbsp;1995 Stage-Graph Representations Evangelos Kranakis, Danny Krizanc, Anil Maheshwari, Marc Noy, Jorg-Rudiger Sack, Jorge Urrutia Abstract We consider graph applications of the well-known paradigm &#8220;killing two birds with one stone&#8221;. In the plane, this gives rise to a stage graph as follows: vertices are the points, and {u, v} is [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11736,"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-12770","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12770","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=12770"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12770\/revisions"}],"predecessor-version":[{"id":12771,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12770\/revisions\/12771"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11736"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=12770"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=12770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}