Unambiguous DNFs and Alon-Saks-Seymour

Kaspars Balodis; Shalev Ben-David; Mika Göös; Siddhartha Jain; Robin Kothari

Unambiguous DNFs and Alon-Saks-Seymour

Computational Complexity 2021-06-08 v2

Authors: Kaspars Balodis , Shalev Ben-David , Mika Göös , Siddhartha Jain , Robin Kothari

Abstract

We exhibit an unambiguous k-DNF formula that requires CNF width $\tilde{\Omega}(k^2)$ , which is optimal up to logarithmic factors. As a consequence, we get a near-optimal solution to the Alon--Saks--Seymour problem in graph theory (posed in 1991), which asks: How large a gap can there be between the chromatic number of a graph and its biclique partition number? Our result is also known to imply several other improved separations in query and communication complexity.

Keywords

unambiguous dnf cnf width alon-saks-seymour problem chromatic number biclique partition number communication complexity

Cite

@article{arxiv.2102.08348,
  title  = {Unambiguous DNFs and Alon-Saks-Seymour},
  author = {Kaspars Balodis and Shalev Ben-David and Mika Göös and Siddhartha Jain and Robin Kothari},
  journal= {arXiv preprint arXiv:2102.08348},
  year   = {2021}
}

Comments

v1: 12 pages, 2 figures. v2: Added an author; improved result; 15 pages

Unambiguous DNFs and Alon-Saks-Seymour

Abstract

Keywords

Cite

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