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Large hypertree width for sparse random hypergraphs

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Listed:
  • Tian Liu

    (Peking University)

  • Chaoyi Wang

    (Peking University)

  • Ke Xu

    (Beihang University)

Abstract

Hypertree width is a graph-theoretic parameter similar to treewidth. It has many equivalent characterizations and many applications. If the hypertree width of the constraint graphs of the instances of a constraint satisfaction problem is bounded by a constant, then the CSP is tractable In this paper, we show that with high probability, hypertree width is large on sparse random $$k$$ k -uniform hypergraphs. Our results provide further theoretical evidence on the hardness of some random constraint satisfaction problems, called Model RB and Model RD, around the satisfiability phase transition points.

Suggested Citation

  • Tian Liu & Chaoyi Wang & Ke Xu, 2015. "Large hypertree width for sparse random hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 531-540, April.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:3:d:10.1007_s10878-013-9704-y
    DOI: 10.1007/s10878-013-9704-y
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    References listed on IDEAS

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    1. Julie Haviland, 2013. "Independent dominating sets in regular graphs," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 120-126, July.
    2. Hung-Lin Fu & Kuo-Ching Huang & Chin-Lin Shiue, 2013. "A note on optimal pebbling of hypercubes," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 597-601, May.
    3. Chun-Hung Liu & Gerard J. Chang, 2013. "Roman domination on strongly chordal graphs," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 608-619, October.
    4. Shenglong Hu & Liqun Qi, 2012. "Algebraic connectivity of an even uniform hypergraph," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 564-579, November.
    5. B. S. Panda & D. Pradhan, 2013. "Minimum paired-dominating set in chordal bipartite graphs and perfect elimination bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 26(4), pages 770-785, November.
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