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Beschreibungen/Notizen
We introduce the class of
k-node label controlled (
NLC)
graphs and the class of
k-NLC trees. Each
k-NLC graph is an undirected tree-structured graph, where
k is a positive integer. The class of
k-NLC trees is a proper subset of the class of
k-NLC graphs. Both classes include many interesting graph families. For instance, each
partial k-tree is a (2
k + 1
− 1)-NLC tree and each co-graph is a 1-NLC graph. Furthermore, we introduce a very general method for the design of polynomial algorithms for NP-complete graph problems, where the input graphs are restricted to tree-structured graphs. We exemplify our method with the
SIMPLE MAX-CUT PROBLEM and the
HAMILTONIAN CIRCUIT PROPERTY on
k-NLC graphs.