Abstract
Tree convex bipartite graphs generalize convex bipartite graphs by associating a tree, instead of a path, with one set of the vertices, such that for every vertex in another set, the neighborhood of this vertex induces a subtree. There are seven graph problems, grouped into three classes of domination, Hamiltonicity and treewidth, which are known to be \(\mathcal {NP}\)-complete for bipartite graphs, but tractable for convex bipartite graphs. We show \(\mathcal {NP}\)-completeness of these problems for tree convex bipartite graphs, even when the associated trees are stars or combs respectively.
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Acknowledgments
This work was first presented at FAW 2014. The help of previous anonymous reviewers has improved our presentation greatly. The work of T. Liu was partially done during the program of Collective Dynamics in Information Systems (2014) in Kavli Institute for Theoretical Physics China at the Chinese Academy of Sciences. Partially supported by Natural Science Foundation of China (Grant Nos. 61370052 and 61370156).
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Chen, H., Lei, Z., Liu, T. et al. Complexity of domination, hamiltonicity and treewidth for tree convex bipartite graphs. J Comb Optim 32, 95–110 (2016). https://doi.org/10.1007/s10878-015-9917-3
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DOI: https://doi.org/10.1007/s10878-015-9917-3