Partition the vertices of a graph into one independent set and one acyclic set |
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Authors: | Aifeng Yang Jinjiang Yuan |
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Institution: | a School of Management, Hefei University of Technology, Hefei Anhui 230009, PR China b Department of Mathematics, Zhengzhou University, Zhengzhou Henan 450052, PR China |
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Abstract: | For a given graph G, if the vertices of G can be partitioned into an independent set and an acyclic set, then we call G a near-bipartite graph. This paper studies the recognition of near-bipartite graphs. We give simple characterizations for those near-bipartite graphs having maximum degree at most 3 and those having diameter 2. We also show that the recognition of near-bipartite graphs is NP-complete even for graphs where the maximum degree is 4 or where the diameter is 4. |
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Keywords: | Near-bipartition Acyclic set Independent set |
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