### The clique-separator graph for chordal graphs

Louis Ibarra
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
We present a new representation of a chordal graph called the clique-separator graph, whose nodes are the maximal cliques and minimal vertex separators of the graph. We present structural properties of the clique-separator graph and additional properties when the chordal graph is an interval graph, proper interval graph, or split graph. We also characterize proper interval graphs and split graphs in terms of the clique-separator graph. We present an algorithm that constructs the
more &raquo; ... graph of a chordal graph in O(n 3 ) time and of an interval graph in O(n 2 ) time, where n is the number of vertices in the graph.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2009.02.006">doi:10.1016/j.dam.2009.02.006</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fmi7qczjujah5owwzxaym33eta">fatcat:fmi7qczjujah5owwzxaym33eta</a> </span>
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