Lower bound on the size-Ramsey number of tight paths

Abstract: The size-Ramsey number

R^{(k)} (H)

of a

k

-uniform hypergraph

H

is the minimum number of edges in a

k

-uniform hypergraph

G

with the property that every `

2

-edge coloring' of

G

contains a monochromatic copy of

H

. For

k g e 2

and

n i n m a t h b b N

, a

k

-uniform tight path on

n

vertices

P_{n}^{(k)}

is defined as a

k

-uniform hypergraph on

n

vertices for which there is an ordering of its vertices such that the edges are all sets of

k

consecutive vertices with respect to this order. We prove a lower bound on the size-Ramsey number of

k

-uniform tight paths, which is, considered assymptotically in both the uniformity

k

and the number of vertices

n

,

.