1 research outputs found
Maximum Weight Independent Sets in Odd-Hole-Free Graphs Without Dart or Without Bull
The Maximum Weight Independent Set (MWIS) Problem on graphs with vertex
weights asks for a set of pairwise nonadjacent vertices of maximum total
weight. Being one of the most investigated and most important problems on
graphs, it is well known to be NP-complete and hard to approximate. The
complexity of MWIS is open for hole-free graphs (i.e., graphs without induced
subgraphs isomorphic to a chordless cycle of length at least five). By applying
clique separator decomposition as well as modular decomposition, we obtain
polynomial time solutions of MWIS for odd-hole- and dart-free graphs as well as
for odd-hole- and bull-free graphs (dart and bull have five vertices, say
, and dart has edges , while bull has edges
). If the graphs are hole-free instead of odd-hole-free then
stronger structural results and better time bounds are obtained