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Tree Convex Bipartite Graphs: \(\mathcal{NP}\)-Complete Domination, Hamiltonicity and Treewidth

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Frontiers in Algorithmics (FAW 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8497))

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Abstract

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 these problems to remain \(\mathcal{NP}\)-complete for tree convex bipartite graphs, even when the associated trees are stars or combs respectively. Tree convex bipartite graphs generalize convex bipartite graphs by associating a tree, instead of a path, on one set of the vertices, such that for every vertex in another set, the neighborhood of this vertex is a subtree.

Partially supported by National 973 Program of China (Grant No. 2010CB328103) and Natural Science Foundation of China (Grant Nos. 61370052 and 61370156).

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Authors and Affiliations

  1. Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing, 100871, China

    Chaoyi Wang, Hao Chen, Ziyang Tang & Tian Liu

  2. School of Mathematical Science, Peking University, Beijing, 100871, China

    Zihan Lei

  3. National Lab of Software Development Environment, Beihang University, Beijing, 100191, China

    Ke Xu

Authors
  1. Chaoyi Wang
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  2. Hao Chen
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  3. Zihan Lei
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  4. Ziyang Tang
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  5. Tian Liu
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  6. Ke Xu
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Texas A&M University, USA

    Jianer Chen

  2. Cornell University, USA

    John E. Hopcroft

  3. School of Information Science and Engineering, Central South University, 410083, Changsha, China

    Jianxin Wang

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Wang, C., Chen, H., Lei, Z., Tang, Z., Liu, T., Xu, K. (2014). Tree Convex Bipartite Graphs: \(\mathcal{NP}\)-Complete Domination, Hamiltonicity and Treewidth. In: Chen, J., Hopcroft, J.E., Wang, J. (eds) Frontiers in Algorithmics. FAW 2014. Lecture Notes in Computer Science, vol 8497. Springer, Cham. https://doi.org/10.1007/978-3-319-08016-1_23

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  • DOI: https://doi.org/10.1007/978-3-319-08016-1_23

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08015-4

  • Online ISBN: 978-3-319-08016-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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