3 research outputs found
Weighted Independent Sets in a Subclass of -free Graphs
The Maximum Weight Independent Set (MWIS) problem on graphs with vertex
weights asks for a set of pairwise nonadjacent vertices of maximum total
weight. The complexity of the MWIS problem for -free graphs is unknown. In
this note, we show that the MWIS problem can be solved in time for
(, banner)-free graphs by analyzing the structure of subclasses of these
class of graphs. This extends the existing results for (, banner)-free
graphs, and (, )-free graphs. Here, denotes the chordless path
on vertices, and a banner is the graph obtained from a chordless cycle on
four vertices by adding a vertex that has exactly one neighbor on the cycle.Comment: arXiv admin note: text overlap with arXiv:1503.0602
The maximum weight stable set problem in (P_6,\mbox{bull})-free graphs
We present a polynomial-time algorithm that finds a maximum weight stable set
in a graph that does not contain as an induced subgraph an induced path on six
vertices or a bull (the graph with vertices and edges )
Independent Sets in Classes Related to Chair/Fork-free Graphs
The Maximum Weight Independent Set (MWIS) problem on graphs with vertex
weights asks for a set of pairwise nonadjacent vertices of maximum total
weight. MWIS is known to be -complete in general, even under various
restrictions. Let be the graph consisting of three induced paths of
lengths with a common initial vertex. The complexity of the MWIS
problem for -free graphs, and for -free graphs are
open. In this paper, we show that the MWIS problem can solved in polynomial
time for (, , co-chair)-free graphs, by analyzing the
structure of the subclasses of this class of graphs. This extends some known
results in the literature.Comment: arXiv admin note: text overlap with arXiv:1504.0540