$F$-factors in hypergraphs via absorption

Details $F$-factors in hypergraphs via absorption $F$-factors in hypergraphs via absorption

2011-05-17

arxiv.org/abs/1105.3411v3

Mathematics

Combinatorics

Fixed some errors in the previous version

Scientific paper

For integers $n \ge k >l \ge 1$ and $k$-graphs $F$, define $t_l^k(n,F)$ to be the smallest integer $d$ such that every $k$-graph $H$ of order $n$ with minimum $l$-degree $\delta_l(H) \ge d $ contains an $F$-factor. A classical theorem of Hajnal and Szemer\'edi implies that $t^2_1(n,K_t) = (1-1/t)n$ for integers $t$. For $k \ge 3$, $t^k_{k-1}(n,K_k^k)$ (the $\delta_{k-1}(H)$ threshold for perfect matchings) has been determined by K\"{u}hn and Osthus (asymptotically) and R\"odl, Ruci\'nski and Szemer\'edi (exactly). In this paper, we generalise the absorption technique of R\"odl, Ruci\'nski and Szemer\'edi to $F$-factors. We determine the asymptotic values of $t^k_1(n,K_k^k(m))$ for $k = 3,4$ and $m \ge 1$. In addition, we show that $t^k_{k-1}(n,K_t^k) \le (1- \frac{1+\gamma}{\binom{t-1}{k-1}}) n$ for $\gamma>0 $ as well as constructing a lower bound on $t^3_{2}(n,K_t^3)$. In particular, we deduce that $t^3_2(n,K_4^3) = (3/4+o(1))n$ answering a question of Pikhurko.

Affiliated with

Also associated with

No associations

Rating

$F$-factors in hypergraphs via absorption does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with $F$-factors in hypergraphs via absorption, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and $F$-factors in hypergraphs via absorption will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-727872