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="" 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="">doi:10.1007/978-3-642-17461-2_17</a> <a target="_blank" rel="external noopener" href="">fatcat:kftdc5kse5bs3g6cpmj4ol56ry</a> </span>
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