{"id":15139,"date":"2022-06-18T20:07:23","date_gmt":"2022-06-19T00:07:23","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=15139"},"modified":"2026-06-08T13:57:52","modified_gmt":"2026-06-08T17:57:52","slug":"tr-248-on-the-number-of-directions-in-visibility-representations-of-graphs","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1994\/tr-248-on-the-number-of-directions-in-visibility-representations-of-graphs\/","title":{"rendered":"TR-248: On the Number of Directions in Visibility Representations of Graphs"},"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-248: On the Number of Directions in Visibility Representations of Graphs\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-1994\/\">Technical Report<\/a>\u00a0<strong>TR-248<\/strong><br>July 1994<\/p>\n\n\n\n<h2 id=\"on-the-number-of-directions-in-visibility-representations-of-graphs\" class=\"wp-block-heading\">On the Number of Directions in Visibility Representations of Graphs<\/h2>\n\n\n\n<p>Evangelos Kranakis, Danny Krizanc, Jorge Urrutia<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>We consider visibility representations of graphs in which the vertices are represented by a collection O of non-overlapping convex regions on the plane. Two points x and y are visible if the straight-line segment xy is not obstructed by any object. Two objects A, B E O are called visible if there exist points x E A, y E B such that x is visible from y. We consider visibility only for a finite set of directions. In such a representation, the given graph is decomposed into a union of unidi\u00adrectional visibility graphs, for the chosen set of directions. This raises the problem of studying the number of directions needed to represent a given graph. We study this number of directions as a graph parameter and obtain sharp upper and lower bounds for the representability of arbitrary graphs.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-248.pdf\">TR-248.pdf<\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report\u00a0TR-248July 1994 On the Number of Directions in Visibility Representations of Graphs Evangelos Kranakis, Danny Krizanc, Jorge Urrutia Abstract We consider visibility representations of graphs in which the vertices are represented by a collection O of non-overlapping convex regions on the plane. Two points x and y are visible if the straight-line segment [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11914,"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-15139","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15139","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=15139"}],"version-history":[{"count":3,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15139\/revisions"}],"predecessor-version":[{"id":24398,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15139\/revisions\/24398"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11914"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=15139"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=15139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}