Finding induced trees

Authors:
N. Derhy;C. Picouleau
Affiliations:
CEDRIC, CNAM, Paris, France;CEDRIC, CNAM, Paris, France
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

Let G=(V(G),E(G)) be a finite connected undirected graph and W@?V(G) a subset of vertices. We are searching for a subset X@?V(G) such that W@?X and the subgraph induced on X is a tree. NP-completeness results and polynomial time algorithms are given assuming that the cardinality of W is fixed or not. Besides we give complexity results when X has to induce a path or when G is a weighted graph. We also consider problems where the cardinality of X has to be minimized.