A median-type condition for graph tiling

Abstract

Komlos [Tiling Turan theorems, Combinatorica, 20,2 (2000), 203218] 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. We show that the minimum degree condition can be relaxed in the sense that we require only a given fraction of vertices to have the prescribed degree.

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