{"id":13089,"date":"2021-12-05T21:00:39","date_gmt":"2021-12-06T02:00:39","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=13089"},"modified":"2026-06-02T14:59:24","modified_gmt":"2026-06-02T18:59:24","slug":"tr-03-07-track-layouts-of-graphs","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2003\/tr-03-07-track-layouts-of-graphs\/","title":{"rendered":"TR-03-07: Track Layouts 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-03-07: Track Layouts of Graphs\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-2003\/\">Technical Report<\/a> TR-03-07<br>\nOctober 2003<\/p>\n\n\n\n<h2 id=\"track-layouts-of-graphs\" class=\"wp-block-heading\">Track Layouts of Graphs<\/h2>\n\n\n\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">Vida Dujmovic &amp; David R. Wood<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<h3>Abstract<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p>A ( k,t ) -track layout of a graph G consists of a (proper) vertex t -colouring of G , a total order of each vertex colour class, and a (non-proper) edge k -colouring such that between each pair of colour classes no two monochromatic edges cross. This structure has recently arisen in the study of three-dimensional graph drawings. This paper presents the beginnings of a theory of track layouts. Our focus is on methods for the manipulation of track layouts, and the relationship between track layouts and other models of graph layout, namely stack and queue layouts, and geometric thickness. In addition we determine the maximum number of edges in a ( k,t ) -track layout, and show how to colour the edges given fixed linear orderings of the vertex colour classes.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-03-07.pdf\">TR-03-07.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-03-07 October 2003 Track Layouts of Graphs Vida Dujmovic &amp; David R. Wood Abstract A ( k,t ) -track layout of a graph G consists of a (proper) vertex t -colouring of G , a total order of each vertex colour class, and a (non-proper) edge k -colouring such that between [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":12314,"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-13089","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13089","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=13089"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13089\/revisions"}],"predecessor-version":[{"id":13090,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13089\/revisions\/13090"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12314"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=13089"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=13089"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}