SIAM Journal on Discrete Mathematics
Journal of Algorithms
Maximum bounded H-matching is Max SNP-complete
Information Processing Letters
The algorithmic aspects of the regularity lemma
Journal of Algorithms
Journal of Combinatorial Theory Series B
An algorithmic version of the blow-up lemma
Random Structures & Algorithms
Proof of the Alon—Yuster conjecture
Discrete Mathematics
Combinatorics, Probability and Computing
Journal of Graph Theory
On the bandwidth conjecture for 3-colourable graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Perfect packings with complete graphs minus an edge
European Journal of Combinatorics
Spanning 3-colourable subgraphs of small bandwidth in dense graphs
Journal of Combinatorial Theory Series B
The Complexity of Perfect Matching Problems on Dense Hypergraphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Research paper: Combinatorial and computational aspects of graph packing and graph decomposition
Computer Science Review
European Journal of Combinatorics
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Let H be any non-bipartite graph. We determine asymptotically the minimum degree of a graph G which ensures that G has a perfect H-packing. More precisely, we determine the smallest number τ having the following property: For every positive constant γ there exists an integer n0 = n0(γ, H) such that every graph G whose order n ≥n0 is divisible by |H| and whose minimum degree is at least (τ + γ) n contains a perfect H-packing. The value of τ depends on the relative sizes of the colour classes in the optimal colourings of H. The proof is algorithmic, which shows that the problem of finding a maximum H-packing is polynomially solvable for graphs G whose minimum degree is at least (τ + γ)n. On the other hand, given any positive constant γ, we show that for infinitely many (non-bipartite) graphs H the corresponding decision problem becomes NP-complete if one considers input graphs G of minimum degree at least (τ - γ)n.