We prove that one can perfectly pack degenerate graphs into complete or dense n-vertex quasirandom graphs, provided that all the degenerate graphs have maximum degree(Formula Presented.)., and in addition Ω(n) of them have at most (1 − Ω(1))n vertices and Ω(n) leaves. This proves Ringel’s conjecture and the Gyárfás Tree Packing Conjecture for all but an exponentially small fraction of trees (or sequences of trees, respectively)
For each of the notions of hypergraph quasirandomness that have been studied, we identify a large cl...
The first part of this thesis concerns perfect matchings and their generalisations. We determine the...
A typical decomposition question asks whether the edges of some graph G can be partitioned into disj...
We prove that there is $c>0$ such that for all sufficiently large $n$, if $T_1,\dots,T_n$ are any tr...
Given D and γ>0, whenever c>0 is sufficiently small and n sufficiently large, if G is a family of D-...
Given D and γ>0, whenever c>0 is sufficiently small and n sufficiently large, if G is a family of D-...
We prove that if T1,…,Tn is a sequence of bounded degree trees such that Ti has i vertices, then Kn ...
We prove that for any pair of constants a>0 and D and for n sufficiently large, every family of tree...
AbstractWe study packings of graphs with given maximal degree. We shall prove that the (hitherto unp...
We prove that for any pair of constants ε > 0 and ∆ and for n sufficiently large, every family of tr...
We prove that for any pair of constants ε > 0 and ∆ and for n sufficiently large, every family of tr...
We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) B...
We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) B...
We prove that given any sequence of $n$ bounded degree trees so that the $j$th tree has $j$ vertices...
Let k ≥ 2 and F be a linear k-uniform hypergraph with v vertices. We prove that if n is sufficiently...
For each of the notions of hypergraph quasirandomness that have been studied, we identify a large cl...
The first part of this thesis concerns perfect matchings and their generalisations. We determine the...
A typical decomposition question asks whether the edges of some graph G can be partitioned into disj...
We prove that there is $c>0$ such that for all sufficiently large $n$, if $T_1,\dots,T_n$ are any tr...
Given D and γ>0, whenever c>0 is sufficiently small and n sufficiently large, if G is a family of D-...
Given D and γ>0, whenever c>0 is sufficiently small and n sufficiently large, if G is a family of D-...
We prove that if T1,…,Tn is a sequence of bounded degree trees such that Ti has i vertices, then Kn ...
We prove that for any pair of constants a>0 and D and for n sufficiently large, every family of tree...
AbstractWe study packings of graphs with given maximal degree. We shall prove that the (hitherto unp...
We prove that for any pair of constants ε > 0 and ∆ and for n sufficiently large, every family of tr...
We prove that for any pair of constants ε > 0 and ∆ and for n sufficiently large, every family of tr...
We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) B...
We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) B...
We prove that given any sequence of $n$ bounded degree trees so that the $j$th tree has $j$ vertices...
Let k ≥ 2 and F be a linear k-uniform hypergraph with v vertices. We prove that if n is sufficiently...
For each of the notions of hypergraph quasirandomness that have been studied, we identify a large cl...
The first part of this thesis concerns perfect matchings and their generalisations. We determine the...
A typical decomposition question asks whether the edges of some graph G can be partitioned into disj...