A High Girth Graph Construction and a Lower Bound for Hitting Set Size for Combinatorial Rectangles

Authors:
L. Sunil Chandran
Affiliations:
-
Venue:
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
Year:
1999

Citing 5
Cited 0

Eigen values and expanders

Combinatorica
Sorting in c log n parallel steps

Combinatorica
More deterministic simulation in logspace

STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Extremal Graph Theory

Extremal Graph Theory
Expander codes

IEEE Transactions on Information Theory - Part 1

Quantified Score

Hi-index	0.00

Visualization

Abstract

We give the following two results. First, we give a deterministic algorithm which constructs a graph of girth logk(n) + O(1) and minimum degree k - 1, taking number of nodes n and the number of edges e = ⌊nk/2⌋ as input. The graphs constructed by our algorithm are expanders of sub-linear sized subsets, that is subsets of size at most nδ, where δ n or k. We also give a lower bound of m/8Ɛ for the size of hitting sets for combinatorial rectangles of volume Ɛ. This result is an improvement of the previously known lower bound, namely Ω(m+1/Ɛ+log(d)). The known upper bound for the size of the hitting set is m poly(log(d)/Ɛ).