Sufficient conditions for perfect mixed tilings

by   Eoin Hurley, et al.

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 Kühn 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 Komlós in a strong sense.



page 1

page 2

page 3

page 4


Perfect domination, Roman domination and perfect Roman domination in lexicographic product graphs

The aim of this paper is to obtain closed formulas for the perfect domin...

On the Existence of Perfect Splitter Sets

Given integers k_1, k_2 with 0< k_1<k_2, the determinations of all posit...

Some New Results on Splitter Sets

Splitter sets have been widely studied due to their applications in flas...

Complementation in t-perfect graphs

Inspired by applications of perfect graphs in combinatorial optimization...

Optimal prevention with possibilistic and mixed background risk

In this paper the effect of posibilistic or mixed background risk on the...

Graphons, mergeons, and so on!

In this work we develop a theory of hierarchical clustering for graphs. ...

Strong Amplifiers of Natural Selection: Proofs

We consider the modified Moran process on graphs to study the spread of ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.