Asymptotic behavior of the chromatic index for hypergraphs
Journal of Combinatorial Theory Series A
The algorithmic aspects of the regularity lemma
Journal of Algorithms
Journal of Combinatorial Theory Series B
Graph Decomposition is NP-Complete: A Complete Proof of Holyer's Conjecture
SIAM Journal on Computing
Proof of the Alon—Yuster conjecture
Discrete Mathematics
A note on a theorem of Erdo's & Gallai
Discrete Mathematics
Integer and fractional packing of families of graphs
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
Minimum H-decompositions of graphs: Edge-critical case
Journal of Combinatorial Theory Series B
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Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let @f"H(n) be the smallest number @f such that any graph G of order n admits an H-decomposition with at most @f parts. Here we determine the asymptotic of @f"H(n) for any fixed graph H as n tends to infinity. The exact computation of @f"H(n) for an arbitrary H is still an open problem. Bollobas [B. Bollobas, On complete subgraphs of different orders, Math. Proc. Cambridge Philos. Soc. 79 (1976) 19-24] accomplished this task for cliques. When H is bipartite, we determine @f"H(n) with a constant additive error and provide an algorithm returning the exact value with running time polynomial in logn.