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Triangle-Tilings in Graphs Without Large Independent Sets

Part of: Graph theory Extremal combinatorics

Published online by Cambridge University Press:  09 May 2018

JÓZSEF BALOGH ,
ANDREW McDOWELL ,
THEODORE MOLLA  and
RICHARD MYCROFT
JÓZSEF BALOGH
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA (e-mail: jobal@math.uiuc.edu)
ANDREW McDOWELL
Affiliation:
Informatics Department, King's College London, London WC2R 2LS, UK (e-mail: andrew.mcdowell@kcl.ac.uk)
THEODORE MOLLA
Affiliation:
University of South Florida, Tampa, FL 33620, USA (e-mail: molla@usf.edu)
RICHARD MYCROFT
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK (e-mail: r.mycroft@bham.ac.uk)
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Abstract

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.

MSC classification

Primary: 05C35: Extremal problems
Secondary: 05C70: Factorization, matching, partitioning, covering and packing 05D40: Probabilistic methods
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Special Issue 4: Special Issue: Oberwolfach Workshop , July 2018 , pp. 449 - 474
Copyright
Copyright © Cambridge University Press 2018 

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