Triangle-Tilings in Graphs Without Large Independent Sets
Digital Object Identifier (DOI)
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.
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Citation / Publisher Attribution
Combinatorics, Probability and Computing, v. 27, issue 4, p. 449-474
Scholar Commons Citation
Balogh, Jozsef; McDowell, Andrew; Molla, Theodore; and Mycroft, Richard, "Triangle-Tilings in Graphs Without Large Independent Sets" (2018). Mathematics and Statistics Faculty Publications. 24.