The complexity of generalized graph colorings

Jason I. Brown
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
Given a graph property P and positive integer k, a P k-coloring of a graph G is an assignment of one of k colors to each vertex of the graph so that the subgraphs induced by each color class have property P. This notion generalizes the standard definition of graph coloring, and has been investigated for many properties. We consider here the complexity of the decision problem. In particular, for the property -G, of not containing an induced subgraph isomorphic to G, we conjecture (and provide
more &raquo; ... ong evidence) that -G k-colorability is NP-complete whenever G has order at least 3 and k 2 2. The techniques rely on new NP-completeness results for hypergraph colorings.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1016/0166-218x(96)00096-0</a> <a target="_blank" rel="external noopener" href="">fatcat:rcb3l3banjgmhdbrgtd3nkc2ya</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href=""> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> </button> </a>