2 research outputs found
Koml贸s's tiling theorem via graphon covers
Komlos [Komlos: Tiling Turan Theorems, Combinatorica, 2000] determined the
asymptotically optimal minimum-degree condition for covering a given proportion
of vertices of a host graph by vertex-disjoint copies of a fixed graph H, thus
essentially extending the Hajnal-Szemeredi theorem which deals with the case
when H is a clique. We give a proof of a graphon version of Komlos's theorem.
To prove this graphon version, and also to deduce from it the original
statement about finite graphs, we use the machinery introduced in [Hladky, Hu,
Piguet: Tilings in graphons, arXiv:1606.03113]. We further prove a stability
version of Komlos's theorem.Comment: 21 pages, 1 figure; accepted to Journal of Graph Theor