Kathie Cameron

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.

Induced matchings in intersection graphs

Abstract An induced matching in a graph G is a set of edges, no two of which meet a common node or are joined by an edge of G ; that is, an induced matching is a matching which forms an induced subgraph. Induced matchings in graph G correspond precisely to independent sets of nodes in the square of the line-graph of G , which we denote by [ L ( G )] 2 . Often, if G has a nice representation as an intersection graph, we can obtain a nice representation of [ L ( G )] 2 as an intersection graph. Then, if the independent set problem is polytime-solvable in [ L ( G )] 2 , the induced matching problem is polytime-solvable in G . In particular, we show that if G is a polygon-circle graph, then so is [ L ( G )] 2 , and the same holds for asteroidal triple-free and interval-filament graphs. It follows that the induced matching problem is polytime-solvable in these classes. Gavrils interval-filament graphs include cocomparability and polygon-circle graphs, and the latter include circle graphs, circular-arc graphs, chordal graphs, and outerplanar graphs.

The Complexity of the List Partition Problem for Graphs

The

Independent packings in structured graphs

k

The graphs with maximum induced matching and maximum matching the same size

-partition problem is as follows: Given a graph

On an adjacency property of almost all graphs

G

Monotone path systems in simple regions

and a positive integer

Coloured matchings in bipartite graphs

k

Coflow polyhedra

, partition the vertices of

On the structure of (pan, even hole)‐free graphs

G