Tiling edge-coloured graphs with few monochromatic bounded-degree graphs

Abstract: We prove that for all integers

D e l t a, r g e q 2

, there is a constant

C = C (D e l t a, r) > 0

such that the following is true for every sequence

m a t h c a l F = F_{1}, F_{2}, l d o t s

of graphs with

v (F_{n}) = n

and

D e l t a (F_{n}) l e q D e l t a

, for each

n i n m a t h b b N

. In every

r

-edge-coloured

K_{n}

, there is a collection of at most

C

monochromatic copies from

m a t h c a l F

whose vertex-sets partition

V (K_{n})

. This makes progress on a conjecture of Grinshpun and S'ark"ozy.

This page was built for publication: Tiling edge-coloured graphs with few monochromatic bounded-degree graphs