R. Sritharan

Finding a maximum induced matching in weakly chordal graphs

An induced matching in a graph G is a set of edges, no two of which meet a common vertex or are joined by an edge of G; that is, an induced matching is a matching which forms an induced subgraph. It is known that finding an induced matching of maximum cardinality in a graph is NP-hard. We show that a maximum induced matching in a weakly chordal graph can be found in polynomial time. This generalizes previously known results for the induced matching problem. This also demonstrates that the maximum induced matching problem in chordal bipartite graphs can be solved in polynomial time while the problem is known to be NP-hard for bipartite graphs in general.

Structure and linear-time recognition of 4-leaf powers

A graph <i>G</i> is the <i>k-leaf power</i> of a tree <i>T</i> if its vertices are leaves of <i>T</i> such that two vertices are adjacent in <i>G</i> if and only if their distance in <i>T</i> is at most <i>k</i>. Then <i>T</i> is a <i>k-leaf root</i> of <i>G</i>. This notion was introduced and studied by Nishimura, Ragde, and Thilikos [2002], motivated by the search for underlying phylogenetic trees. Their results imply an <i>O</i>(<i>n</i>³)-time recognition algorithm for 4-leaf powers. Recently, Rautenbach [2006] as well as Dom et al. [2005] characterized 4-leaf powers without true twins in terms of forbidden subgraphs. We give new characterizations for 4-leaf powers and squares of trees by a complete structural analysis. As a consequence, we obtain a conceptually simple linear-time recognition of 4-leaf powers.

The Complexity of the List Partition Problem for Graphs

The

On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs

k

Improved algorithms for weakly chordal graphs

-partition problem is as follows: Given a graph

Chordal bipartite completion of colored graphs

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Finding houses and holes in graphs

and a positive integer

The induced matching and chain subgraph cover problems for convex bipartite graphs

k

Recognition of some perfectly orderable graph classes

, partition the vertices of

Cycle Extendability and Hamiltonian Cycles in Chordal Graph Classes

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