Everything about Packing in a hypergraph
In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges in each subset share any vertex. There are two famous algorithms to achieve asymptotically optimal packing in k-uniform hypergraphs. One of them is a random greedy algorithm which was proposed by Joel Spencer. He used a branching process to formally prove the optimal achievable bound under some side conditions. The other algorithm is called the Rödl nibble and was proposed by Vojtěch Rödl et al. They showed that the achievable packing by the Rödl nibble is in some sense close to that of the random greedy algorithm. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Packing in a hypergraphA 5-minute orientation
- Skim a recent paper: Maximum Packing of λ-Fold Complete 3-Uniform Hypergraph with a Special TetrahedronInfluential work since 2022
- Read the landmark paper: Hypergraph Packing and Sparse Bipartite Ramsey NumbersCited 16 times
- Go sideways: KernelizationA closely related topic
- Go sideways: Erdős–Stone theoremA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Hypergraph Packing and Sparse Bipartite Ramsey Numbers
Hypergraph Packing and Graph Embedding
Nearly-perfect hypergraph packing is in NC
Packing, covering and decomposing of a complete uniform hypergraph into delta-systems
Faster algorithms for sparse ILP and hypergraph multi-packing/multi-cover problems
A note on packing of two copies of a hypergraph
On packing of two copies of a hypergraph
A Hypergraph Version of a Graph Packing Theorem by Bollobás and Eldridge
🆕 Influential since 2022
📚 Books worth reading
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