Affiliation:
1. Alfréd Rényi Institute of Mathematics
2. University of Birmingham
3. Alfréd Rényi Institute of Mathematics , Lab. of Combinatorial and Geometric Structures , Moscow Inst. of Physics and Technology
Abstract
Abstract
In this short note we consider the oriented vertex Turán problem in the hypercube: for a fixed oriented graph
F
→
\vec F
, determine the maximum cardinality
e
x
v
(
F
→
,
Q
→
n
)
e{x_v}\left( {\vec F,{{\vec Q}_n}} \right)
of a subset U of the vertices of the oriented hypercube
Q
→
n
{\vec Q_n}
such that the induced subgraph
Q
→
n
[
U
]
{\vec Q_n}\left[ U \right]
does not contain any copy of
F
→
\vec F
. We obtain the exact value of
e
x
v
(
P
k
,
→
Q
n
→
)
e{x_v}\left( {\overrightarrow {{P_k},} \,\overrightarrow {{Q_n}} } \right)
for the directed path
P
k
→
\overrightarrow {{P_k}}
, the exact value of
e
x
v
(
V
2
→
,
Q
n
→
)
e{x_v}\left( {\overrightarrow {{V_2}} ,\,\overrightarrow {{Q_n}} } \right)
for the directed cherry
V
2
→
\overrightarrow {{V_2}}
and the asymptotic value of
e
x
v
(
T
→
,
Q
n
→
)
e{x_v}\left( {\overrightarrow T ,\overrightarrow {{Q_n}} } \right)
for any directed tree
T
→
\vec T
.
Cited by
1 articles.
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