{"id":2684,"date":"2026-03-19T18:32:25","date_gmt":"2026-03-19T18:32:25","guid":{"rendered":"https:\/\/iesmgkorreas.com\/revistasapereaude2024\/?p=2684"},"modified":"2026-03-19T18:34:32","modified_gmt":"2026-03-19T18:34:32","slug":"donde-construimos-el-hospital-una-solucion-matematica-basada-en-distancias","status":"publish","type":"post","link":"https:\/\/iesmgkorreas.com\/revistasapereaude2024\/?p=2684","title":{"rendered":"\u00bfD\u00f3nde construimos el hospital? Una soluci\u00f3n matem\u00e1tica basada en distancias"},"content":{"rendered":"\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<blockquote class=\"wp-block-quote is-style-plain has-background is-layout-flow wp-block-quote-is-layout-flow\" style=\"background:linear-gradient(190deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%)\">\n<p class=\"has-medium-font-size\">El estudio de los grafos naci\u00f3 en 1736 cuando Leonhard Euler resolvi\u00f3 el problema de los siete puentes de K\u00f6nigsberg, introduciendo el uso de v\u00e9rtices y aristas para representar relaciones. Aqu\u00ed se sentaron las bases de la teor\u00eda de grafos y su importancia en matem\u00e1ticas e inform\u00e1tica.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<figure class=\"wp-block-image aligncenter size-full is-style-default\"><img fetchpriority=\"high\" decoding=\"async\" width=\"269\" height=\"187\" src=\"https:\/\/iesmgkorreas.com\/revistasapereaude2024\/wp-content\/uploads\/2026\/03\/image-1.png\" alt=\"\" class=\"wp-image-2685\"\/><\/figure>\n<\/div>\n<\/div>\n<\/blockquote>\n<\/div>\n\n\n\n<p><\/p>\n<\/div>\n\n\n\n<blockquote class=\"wp-block-quote has-background is-layout-flow wp-block-quote-is-layout-flow\" style=\"background:linear-gradient(190deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%)\">\n<p class=\"has-medium-font-size\">Un <strong>grafo<\/strong> es una estructura matem\u00e1tica que se usa para representar relaciones entre objetos.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Sus <strong>elementos <\/strong>son los v\u00e9rtices y aristas.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">La <strong>valencia <\/strong>de un v\u00e9rtice es el n\u00famero de aristas que inciden en \u00e9l.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Existen muchos tipos de grafos como el grafo ciclo:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">El <strong>grafo ciclo<\/strong> es el camino que empieza y termina en el mismo v\u00e9rtice.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" width=\"240\" height=\"210\" src=\"https:\/\/iesmgkorreas.com\/revistasapereaude2024\/wp-content\/uploads\/2026\/03\/image-2.png\" alt=\"\" class=\"wp-image-2686\" style=\"width:194px;height:auto\"\/><\/figure>\n<\/blockquote>\n\n\n\n<p><\/p>\n\n\n\n<blockquote class=\"wp-block-quote has-background is-layout-flow wp-block-quote-is-layout-flow\" style=\"background:linear-gradient(190deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%)\">\n<p class=\"has-medium-font-size\">Un <strong>grafo euleriano<\/strong> es un grafo que tiene un circuito euleriano, esto significa:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u00a0-Se pueden recorrer todas las aristas pasando por cada una de ellas una sola vez.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u00a0&#8211; Partimos y acabamo en el mismo v\u00e9rtice.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Muchos habr\u00e9is jugado a dibujar esta casita sin levantar el l\u00e1piz ni repetir ninguna arista. Aqu\u00ed ten\u00e9is una soluci\u00f3n. <\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" width=\"225\" height=\"225\" src=\"https:\/\/iesmgkorreas.com\/revistasapereaude2024\/wp-content\/uploads\/2026\/03\/image-3.png\" alt=\"\" class=\"wp-image-2687\" style=\"width:213px;height:auto\" srcset=\"https:\/\/iesmgkorreas.com\/revistasapereaude2024\/wp-content\/uploads\/2026\/03\/image-3.png 225w, https:\/\/iesmgkorreas.com\/revistasapereaude2024\/wp-content\/uploads\/2026\/03\/image-3-150x150.png 150w, https:\/\/iesmgkorreas.com\/revistasapereaude2024\/wp-content\/uploads\/2026\/03\/image-3-50x50.png 50w\" sizes=\"(max-width: 225px) 100vw, 225px\" \/><\/figure>\n<\/blockquote>\n\n\n\n<div class=\"wp-block-group has-background is-vertical is-layout-flex wp-container-core-group-is-layout-fe9cc265 wp-block-group-is-layout-flex\" style=\"background:linear-gradient(190deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%)\">\n<p class=\"has-medium-font-size\"><em>Esto se puede realizar en cualquier grafo si todas las valencias de sus v\u00e9rtices son n\u00fameros pares.<\/em><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Un <strong>grafo semieuleriano<\/strong> es un grafo que tiene un camino euleriano pero no un circuito, es decir:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">&#8211; Se pueden recorrer todas las aristas pasando por todas ellas una sola vez.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">&#8211; Solamente se puede realizar empezando y terminando en v\u00e9rtices distintos (esos dos v\u00e9rtices podr\u00edan tener valencia impar, ninguno m\u00e1s)<\/p>\n<\/div>\n\n\n\n<p><\/p>\n\n\n\n<blockquote class=\"wp-block-quote has-background is-layout-flow wp-block-quote-is-layout-flow\" style=\"background:linear-gradient(190deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%)\">\n<p class=\"has-medium-font-size\">Un <strong>grafo hamiltoniano <\/strong>es un grafo que tiene un ciclo hamiltoniano, es decir, un recorrido que visita todos los v\u00e9rtices exactamente una vez y vuelve al inicio<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"323\" height=\"259\" src=\"https:\/\/iesmgkorreas.com\/revistasapereaude2024\/wp-content\/uploads\/2026\/03\/image-6.png\" alt=\"\" class=\"wp-image-2692\" style=\"width:244px;height:auto\" srcset=\"https:\/\/iesmgkorreas.com\/revistasapereaude2024\/wp-content\/uploads\/2026\/03\/image-6.png 323w, https:\/\/iesmgkorreas.com\/revistasapereaude2024\/wp-content\/uploads\/2026\/03\/image-6-300x241.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/figure>\n<\/blockquote>\n\n\n\n<p><\/p>\n\n\n\n<blockquote class=\"wp-block-quote has-background is-layout-flow wp-block-quote-is-layout-flow\" style=\"background:linear-gradient(190deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%)\">\n<p class=\"has-medium-font-size\"><strong><em><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Usamos los grafos para tomar decisiones democr\u00e1ticas.<\/mark><\/em><\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">En una comarca se va a construir un hospital que pueda atender a los 8 pueblos principales que la forman.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Tenemos que decidir en qu\u00e9 pueblo construir el hospital tratando de ser justos en su elecci\u00f3n, atendiendo a las distancias que habr\u00eda que recorrer desde cada uno. \u00bfHay alguna forma de comparar las distancias y poder decidir?<\/p>\n\n\n\n<p class=\"has-medium-font-size\">S\u00ed, en teor\u00eda de grafos contamos con el <strong>algoritmo de Dijkstra<\/strong> que nos permite calcular todas las distancias desde un v\u00e9rtice (pueblo) a todos los dem\u00e1s.<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Fuenteclara (A)<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Seval (B)<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Valleverde (C)<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Encinar (D)<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>R\u00edar (E)<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Altena (F)<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Niole (G)<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Jeval (H)<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">El algoritmo consiste en crear una tabla con todos los v\u00e9rtices en la que se van apuntando, sumando distancias y eligiendo el camino m\u00e1s corto para llegar a un v\u00e9rtice fijado. Adem\u00e1s, el camino me indicar\u00e1 la distancia m\u00e1s corta. As\u00ed, podremos elegir democr\u00e1ticamente el pueblo en el que construir el hospital.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/iesmgkorreas.com\/revistasapereaude2024\/wp-content\/uploads\/2026\/03\/image-7-1024x575.png\" alt=\"\" class=\"wp-image-2693\"\/><\/figure>\n\n\n\n<p><\/p>\n<\/blockquote>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>El estudio de los grafos naci\u00f3 en 1736 cuando Leonhard Euler resolvi\u00f3 el problema 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