Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the maximum number of spanning copies of an orientation in a
  tournament   For an orientation $H$ with $n$ vertices, let $T(H)$ denote the maximum
possible number of labeled copies of $H$ in an $n$-vertex tournament. It is
easily seen that $T(H) \ge n!/2^{e(H)}$ as the latter is the expected number of
such copies in a random tournament. For $n$ odd, let $R(H)$ denote the maximum
possible number of labeled copies of $H$ in an $n$-vertex regular tournament.
Adler et al. proved that, in fact, for $H=C_n$ the directed Hamilton cycle,
$T(C_n) \ge (e-o(1))n!/2^{n}$ and it was observed by Alon that already $R(C_n)
\ge (e-o(1))n!/2^{n}$. Similar results hold for the directed Hamilton path
$P_n$. In other words, for the Hamilton path and cycle, the lower bound derived
from the expectation argument can be improved by a constant factor. In this
paper we significantly extend these results and prove that they hold for a
larger family of orientations $H$ which includes all bounded degree Eulerian
orientations and all bounded degree balanced orientations, as well as many
others. One corollary of our method is that for any $k$-regular orientation $H$
with $n$ vertices, $T(H) \ge (e^k-o(1))n!/2^{e(H)}$ and in fact, for $n$ odd,
$R(H) \ge (e^k-o(1))n!/2^{e(H)}$.

26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas