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Complexity of domination, hamiltonicity and treewidth for tree convex bipartite graphs

Author

Listed:
  • Hao Chen

    (Peking University)

  • Zihan Lei

    (Peking University)

  • Tian Liu

    (Peking University)

  • Ziyang Tang

    (Peking University)

  • Chaoyi Wang

    (Peking University)

  • Ke Xu

    (Beihang University)

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 $$\mathcal {NP}$$ NP -complete for bipartite graphs, but tractable for convex bipartite graphs. We show $$\mathcal {NP}$$ NP -completeness of these problems for tree convex bipartite graphs, even when the associated trees are stars or combs respectively.

Suggested Citation

  • Hao Chen & Zihan Lei & Tian Liu & Ziyang Tang & Chaoyi Wang & Ke Xu, 2016. "Complexity of domination, hamiltonicity and treewidth for tree convex bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 95-110, July.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:1:d:10.1007_s10878-015-9917-3
    DOI: 10.1007/s10878-015-9917-3
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    References listed on IDEAS

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    1. Lei Chen & Changhong Lu & Zhenbing Zeng, 2010. "Labelling algorithms for paired-domination problems in block and interval graphs," Journal of Combinatorial Optimization, Springer, vol. 19(4), pages 457-470, May.
    2. Tian Liu & Zhao Lu & Ke Xu, 2015. "Tractable connected domination for restricted bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 247-256, January.
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    Cited by:

    1. D. H. Aneesh & A. Mohanapriya & P. Renjith & N. Sadagopan, 2022. "Steiner tree in k-star caterpillar convex bipartite graphs: a dichotomy," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1221-1247, September.
    2. B. S. Panda & Arti Pandey & Juhi Chaudhary & Piyush Dane & Manav Kashyap, 0. "Maximum weight induced matching in some subclasses of bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-20.
    3. B. S. Panda & Arti Pandey & Juhi Chaudhary & Piyush Dane & Manav Kashyap, 2020. "Maximum weight induced matching in some subclasses of bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 40(3), pages 713-732, October.

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