Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: More about sparse halves in triangle-free graphs   One of Erdos's conjectures states that every triangle-free graph on $n$
vertices has an induced subgraph on $n/2$ vertices with at most $n^2/50$ edges.
We report several partial results towards this conjecture. In particular, we
establish the new bound $\frac{27}{1024}n^2$ on the number of edges in general
case. We completely prove the conjecture for graphs of girth $\geq 5$, for
graphs with independence number $\geq 2n/5$ and for strongly regular graphs.
Each of these three classes includes both known (conjectured) extremal
configurations, the 5-cycle and the Petersen graph.

35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn