On the maximum independent set problem in subclasses of subcubic graphs
Résumé
It is known that the maximum independent set problem is NP-complete
for subcubic graphs, i.e. graphs of vertex degree at most 3. Moreover, the
problem is NP-complete for 3-regular Hamiltonian graphs and for
H
-free
subcubic graphs whenever
H
contains a connected component which is not
a tree with at most 3 leaves. We show that if every connected component of
H
is a tree with at most 3 leaves and at most 7 vertices, then the problem can
be solved for
H
-free subcubic graphs in polynomial time. We also strengthen
the NP-completeness of the problem on 3-regular Hamiltonian graphs by
showing that the problem is APX-complete in this class