## On Even-Degree Subgraphs of Linear Hypergraphs

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##### Date

2012-03##### Author

Dellamonica, Domingos Jr

Haxell, Penny E.

Łuczak, Tomasz

Muyabi, Dhruv

Nagle, Brendan

Person, Yury

Rödl, Vojtech

Schacht, Mathias

Verstraëte, Jacques

##### Publisher

Cambridge University Press##### Metadata

Show full item record##### Abstract

A subgraph of a hypergraph H is even if all its degrees are positive even integers, and b-bounded if it has maximum degree at most b. Let f(b)(n) denote the maximum number of edges in a linear n-vertex 3-uniform hypergraph which does not contain a b-bounded even subgraph. In this paper, we show that if b >= 12, then
n log n/3b log log n <= f(b)(n) <= Bn(log n)(2)
for some absolute constant B, thus establishing f(b)(n) up to polylogarithmic factors. This leaves open the interesting case b = 2, which is the case of 2-regular subgraphs. We are able to show for some constants c, C > 0 that
cn log n <= f2( n) <= Cn(3/2)(log n)(5).
We conjecture that f(2)(n) = n(1+o(1)) as n -> infinity.