pith. sign in

arxiv: 2201.03944 · v3 · pith:B2R26Z32new · submitted 2022-01-11 · 🧮 math.CO · cs.DM

Sufficient conditions for perfect mixed tilings

classification 🧮 math.CO cs.DM
keywords conditionsdegreegraphsperfectsufficienttilingsmixedaforementioned
0
0 comments X
read the original abstract

We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs $H$ with components of sublinear order. As a corollary, we recover and extend the work of K\"uhn and Osthus regarding sufficient minimum degree conditions for perfect $F$-tilings (for an arbitrary fixed graph $F$) by replacing the $F$-tiling with the aforementioned graphs $H$. Moreover, we obtain analogous results for degree sequences and in the setting of uniformly dense graphs. Finally, we asymptotically resolve a conjecture of Koml\'os in a strong sense.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.