{"paper":{"title":"The ratio of domination and independent domination numbers on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bing Wei, Shaohui Wang","submitted_at":"2016-10-05T18:57:57Z","abstract_excerpt":"Let $\\gamma(G)$ and $i(G)$ be the domination number and the independent domination number of $G$, respectively. In 1977, Hedetniemi and Mitchell began with the comparison of of $i(G)$ and $\\gamma(G)$ and recently Rad and Volkmann posted a conjecture that $i(G)/ \\gamma(G) \\leq \\Delta(G)/2$, where $\\Delta(G)$ is the maximum degree of $G$. In this work, we prove the conjecture for trees and provide the graph achieved the sharp bound."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01568","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}