### New Min-Max Theorems for Weakly Chordal and Dually Chordal Graphs [chapter]

Arthur H. Busch, Feodor F. Dragan, R. Sritharan
<span title="">2010</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
A distance-k matching in a graph G is matching M in which the distance between any two edges of M is at least k. A distance-2 matching is more commonly referred to as an induced matching. In this paper, we show that when G is weakly chordal, the size of the largest induced matching in G is equal to the minimum number of co-chordal subgraphs of G needed to cover the edges of G, and that the co-chordal subgraphs of a minimum cover can be found in polynomial time. Using similar techniques, we show
more &raquo; ... that the distance-k matching problem for k > 1 is tractable for weakly chordal graphs when k is even, and is NP-hard when k is odd. For dually chordal graphs, we use properties of hypergraphs to show that the distance-k matching problem is solvable in polynomial time whenever k is odd, and NP-hard when k is even. Motivated by our use of hypergraphs, we define a class of hypergraphs which lies strictly in between the well studied classes of acyclic hypergraphs and normal hypergraphs.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-17461-2_17">doi:10.1007/978-3-642-17461-2_17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kftdc5kse5bs3g6cpmj4ol56ry">fatcat:kftdc5kse5bs3g6cpmj4ol56ry</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829061152/http://www.cs.kent.edu/~dragan/Papers2010+/COCOA-2010.pdf" 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="https://blobs.fatcat.wiki/thumbnail/pdf/ec/f1/ecf164408ffc1a67602997685335326b515cce7d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-17461-2_17"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>