Deepak Bal - Profile on Academia.edu (original) (raw)
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Papers by Deepak Bal
Arxiv preprint arXiv:1104.3158, Jan 1, 2011
In this note, we determine the maximum number of edges of a k-uniform hypergraph, k ≥ 3, with a u... more In this note, we determine the maximum number of edges of a k-uniform hypergraph, k ≥ 3, with a unique perfect matching. This settles a conjecture proposed
Arxiv preprint arXiv:1102.1488, Jan 1, 2011
We say that a k-uniform hypergraph C is a Hamilton cycle of type ℓ, for some 1 ≤ ℓ ≤ k, if there ... more We say that a k-uniform hypergraph C is a Hamilton cycle of type ℓ, for some 1 ≤ ℓ ≤ k, if there exists a cyclic ordering of the vertices of C such that every edge consists of k consecutive vertices and for every pair of consecutive edges E i−1 , E i in C (in the natural ordering of the edges) we have |E i−1 \ E i | = ℓ. We define a class of (ǫ, p)-regular hypergraphs, that includes random hypergraphs, for which we can prove the existence of a decomposition of almost all edges into type ℓ Hamilton cycles, where ℓ < k/2. * Research supported in part by NSF award DMS-0753472.
Information and Computation, Jan 1, 2008
Arxiv preprint arXiv:1104.3158, Jan 1, 2011
In this note, we determine the maximum number of edges of a k-uniform hypergraph, k ≥ 3, with a u... more In this note, we determine the maximum number of edges of a k-uniform hypergraph, k ≥ 3, with a unique perfect matching. This settles a conjecture proposed
Arxiv preprint arXiv:1102.1488, Jan 1, 2011
We say that a k-uniform hypergraph C is a Hamilton cycle of type ℓ, for some 1 ≤ ℓ ≤ k, if there ... more We say that a k-uniform hypergraph C is a Hamilton cycle of type ℓ, for some 1 ≤ ℓ ≤ k, if there exists a cyclic ordering of the vertices of C such that every edge consists of k consecutive vertices and for every pair of consecutive edges E i−1 , E i in C (in the natural ordering of the edges) we have |E i−1 \ E i | = ℓ. We define a class of (ǫ, p)-regular hypergraphs, that includes random hypergraphs, for which we can prove the existence of a decomposition of almost all edges into type ℓ Hamilton cycles, where ℓ < k/2. * Research supported in part by NSF award DMS-0753472.
Information and Computation, Jan 1, 2008