Topological graph theory
Finding a maximum-genus graph imbedding
Journal of the ACM (JACM)
Partitions of graphs into one or two independent sets and cliques
Discrete Mathematics
Polynomial algorithms for the maximum stable set problem on particular classes of P5-free graphs
Information Processing Letters
Efficient algorithms for a mixed K-partition problem of graphs without specifying bases
Theoretical Computer Science
Clique and anticlique partitions of graphs
Discrete Mathematics
The complexity of some problems related to Graph 3-COLORABILITY
Discrete Applied Mathematics
Graph Ear Decompositions and Graph Embeddings
SIAM Journal on Discrete Mathematics
Graph Theory With Applications
Graph Theory With Applications
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A stable set of a graph is a vertex set in which any two vertices are not adjacent. It was proven in [A. Brandstadt, V.B. Le, T. Szymczak, The complexity of some problems related to graph 3-colorability, Discrete Appl. Math. 89 (1998) 59-73] that the following problem is NP-complete: Given a bipartite graph G, check whether G has a stable set S such thatG-Sis a tree. In this paper we prove the following problem is polynomially solvable: Given a graph G with maximum degree 3 and containing no vertices of degree 2, check whether G has a stable set S such thatG-Sis a tree. Thus we partly answer a question posed by the authors in the above paper. Moreover, we give some structural characterizations for a graph G with maximum degree 3 that has a stable set S such that G-S is a tree.