{"id":5531,"date":"2020-07-25T07:53:20","date_gmt":"2020-07-25T14:53:20","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=5531"},"modified":"2020-07-25T09:15:45","modified_gmt":"2020-07-25T16:15:45","slug":"the-874-vertex-4461-edge-5-color-graph-solution-to-the-hadwiger-nelson-problem","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2020\/07\/25\/the-874-vertex-4461-edge-5-color-graph-solution-to-the-hadwiger-nelson-problem\/","title":{"rendered":"5-color graph solutions to the Hadwiger\u2013Nelson problem"},"content":{"rendered":"\n<p>These are a simple animated visualizations I created while studying the problem. They contain a sequence of 2s frames starting at 130 vertices and incrementing 62. The red numbered text are the first few starting vertex numbers showing the hexagonal structure of the construction. On the left is a list of sorted and color coded vertices by the number of edges on a vertex for that frame&#8217;s shown vertices (it also lists in the right column the number of vertices with that number of edges &amp; color). The solution data was obtained from: <a href=\"https:\/\/github.com\/marijnheule\/CNP-SAT\">https:\/\/github.com\/marijnheule\/CNP-SAT<\/a><\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"The 510 vertex \/ 2504 edge 5-color graph solution to the Hadwiger\u2013Nelson problem\" width=\"474\" height=\"267\" src=\"https:\/\/www.youtube.com\/embed\/MVEXMuA1kuY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption>The 510 vertex \/ 2504 edge 5-color graph solution to the Hadwiger\u2013Nelson problem<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"The 874 vertex \/ 4461 edge  5-color graph solution to the Hadwiger\u2013Nelson problem\" width=\"474\" height=\"267\" src=\"https:\/\/www.youtube.com\/embed\/N4k_fwd8x9M?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption>The 874 vertex \/ 4461 edge 5-color graph solution to the Hadwiger\u2013Nelson problem<\/figcaption><\/figure>\n\n\n\n<p>Here is a <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/5-color-solutions.nb\">link <\/a>to a Mathematica Notebook (50Mb) that has interactive  ListAnimated graphs with vertex data (vertex number, symbolic and numeric coordinates, number of edges on the vertex in the frame) in Tooltip on mouseover.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>These are a simple animated visualizations I created while studying the problem. They contain a sequence of 2s frames starting at 130 vertices and incrementing 62. The red numbered text are the first few starting vertex numbers showing the hexagonal structure of the construction. On the left is a list of sorted and color coded &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2020\/07\/25\/the-874-vertex-4461-edge-5-color-graph-solution-to-the-hadwiger-nelson-problem\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">5-color graph solutions to the Hadwiger\u2013Nelson problem<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-5531","post","type-post","status-publish","format-standard","hentry","category-physics"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.8 - aioseo.com -->\n\t<meta name=\"description\" content=\"These are a simple animated visualizations I created while studying the problem. They contain a sequence of 2s frames starting at 130 vertices and incrementing 62. The red numbered text are the first few starting vertex numbers showing the hexagonal structure of the construction. On the left is a list of sorted and color coded\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"jgmoxness\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/theoryofeverything.org\/theToE\/2020\/07\/25\/the-874-vertex-4461-edge-5-color-graph-solution-to-the-hadwiger-nelson-problem\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 4.9.8\" \/>\n\t\t<meta property=\"og:locale\" content=\"en_US\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Visualizing a Theory of Everything! - Dedicated to the pursuit of beauty and Truth in Nature!\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"5-color graph solutions to the Hadwiger\u2013Nelson problem - Visualizing a Theory of Everything!\" \/>\n\t\t<meta property=\"og:description\" content=\"These are a simple animated visualizations I created while studying the problem. They contain a sequence of 2s frames starting at 130 vertices and incrementing 62. The red numbered text are the first few starting vertex numbers showing the hexagonal structure of the construction. On the left is a list of sorted and color coded\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/theoryofeverything.org\/theToE\/2020\/07\/25\/the-874-vertex-4461-edge-5-color-graph-solution-to-the-hadwiger-nelson-problem\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2020-07-25T14:53:20+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2020-07-25T16:15:45+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary\" \/>\n\t\t<meta name=\"twitter:title\" content=\"5-color graph solutions to the Hadwiger\u2013Nelson problem - Visualizing a Theory of Everything!\" \/>\n\t\t<meta name=\"twitter:description\" content=\"These are a simple animated visualizations I created while studying the problem. They contain a sequence of 2s frames starting at 130 vertices and incrementing 62. The red numbered text are the first few starting vertex numbers showing the hexagonal structure of the construction. 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