Triangle-tilings in graphs without large independent sets

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Colleges, School and Institutes

External organisations

  • University of Illinois
  • University of South Florida Tampa


We study the minimum degree necessary to guarantee the existence of perfect and almost-perfect triangle-tilings in an n-vertex graph G with sublinear independence number. In this setting, we show that if δ(G)≥n/3+o(n) then G has a triangle-tiling covering all but at most four vertices. Also, for every r≥5, we asymptotically determine the minimum degree threshold for a perfect triangle-tiling under the additional assumptions that G is Kr-free and n is divisible by 3.


Original languageEnglish
Number of pages24
JournalCombinatorics, Probability and Computing
Early online date9 May 2018
Publication statusE-pub ahead of print - 9 May 2018