4 research outputs found
A note on "Folding wheels and fans."
In S.Gervacio, R.Guerrero and H.Rara, Folding wheels and fans, Graphs and
Combinatorics 18 (2002) 731-737, the authors obtain formulas for the clique
numbers onto which wheels and fans fold. We present an interpolation theorem
which generalizes their theorems 4.2 and 5.2. We show that their formula for
wheels is wrong. We show that for threshold graphs, the achromatic number and
folding number coincides with the chromatic number
On retracts, absolute retracts, and folds in cographs
Let G and H be two cographs. We show that the problem to determine whether H
is a retract of G is NP-complete. We show that this problem is fixed-parameter
tractable when parameterized by the size of H. When restricted to the class of
threshold graphs or to the class of trivially perfect graphs, the problem
becomes tractable in polynomial time. The problem is also soluble when one
cograph is given as an induced subgraph of the other. We characterize absolute
retracts of cographs.Comment: 15 page