Clique-factors in graphs with sublinear ℓ-independence number

2022/03/04 by Han, Jie, Hu, Ping, Wang, Guanghui +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.02169

Abstract

Given a graph G and an integer ℓ≥ 2, we denote by α_ℓ(G) the maximum size of a K_ℓ-free subset of vertices in V(G). A recent question of Nenadov and Pehova asks for determining the best possible minimum degree conditions forcing clique-factors in n-vertex graphs G with α_ℓ(G) = o(n), which can be seen as a Ramsey--Turán variant of the celebrated Hajnal--Szemerédi theorem. In this paper we find the asymptotical sharp minimum degree threshold for K_r-factors in n-vertex graphs G with α_ℓ(G)=n^1-o(1) for all r≥ ℓ≥ 2.

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