https://jinerx.github.io/tags/graph-theory/Recent content in Graph Theory on JinerX blogHugo -- gohugo.ioen-us© 2026 Jędrzej SajnógWed, 18 Mar 2026 16:25:43 +0100https://jinerx.github.io/learning_log/minimum-spanning-tree/Wed, 18 Mar 2026 16:25:43 +0100https://jinerx.github.io/learning_log/minimum-spanning-tree/<p>Here we&rsquo;re going to cover what are Minimum Spanning Trees (MSTs), methods for finding them and use cases.</p> <h2 class="relative group">What is a tree? <div id="what-is-a-tree" class="anchor"></div> <span class="absolute top-0 w-6 transition-opacity opacity-0 -start-6 not-prose group-hover:opacity-100 select-none"> <a class="text-primary-300 dark:text-neutral-700 !no-underline" href="#what-is-a-tree" aria-label="Anchor">#</a> </span> </h2> <p>In graph theory we call graph $T=(V,E)$ a tree if it is connected and it doesn&rsquo;t have any cycles.</p> <div class="admonition relative overflow-hidden rounded-lg border-l-4 my-3 px-4 py-3 shadow-sm" data-type="info"> <div class="flex items-center gap-2 font-semibold text-inherit"> <div class="flex shrink-0 h-5 w-5 items-center justify-center text-lg"><span class="relative block icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256 0C114.6 0 0 114.6 0 256s114.6 256 256 256s256-114.6 256-256S397.4 0 256 0zM256 128c17.67 0 32 14.33 32 32c0 17.67-14.33 32-32 32S224 177.7 224 160C224 142.3 238.3 128 256 128zM296 384h-80C202.8 384 192 373.3 192 360s10.75-24 24-24h16v-64H224c-13.25 0-24-10.75-24-24S210.8 224 224 224h32c13.25 0 24 10.75 24 24v88h16c13.25 0 24 10.75 24 24S309.3 384 296 384z"/></svg> </span></div> <div class="grow"> Forrest </div> </div><div class="admonition-content mt-3 text-base leading-relaxed text-inherit"><p>We call a graph with no cycles a forrest (contrary to the tree it doesn&rsquo;t need to be connected). In a forrest each <strong>connected component</strong> is a tree.</p>