Báo cáo toán học: "On the number of perfect matchings and Hamilton cycles in -regular non-bipartite graphs" ppsx
Báo cáo toán học: "On the number of perfect matchings and Hamilton cycles in -regular non-bipartite graphs" ppsx
... n)k
−1
φ(k).
In either case, the inequality in part 1 of the lemma holds.
On the number of perfect matchings and Hamilton
cycles in -regular non-bipartite graphs
Alan Frieze
∗
Department of Mathematical ... of combinatorics 7 (2000), #R57 4
3 Hamilton Cycles
A Hamilton cycle is the union of two perfect matchings and so h(G) ≤
1
2
m(G)
2
an...
Báo cáo toán học: "On the number of possible row and column sums of 0,1-matrices" pps
... ,a
n
)=
a(x)inN
n+1
.Wenotethat|a| = m,andwrite
m
a
for the multinomial coefficient
m!
a
0
!···a
n
!
With this notation, we have the following lemma.
Lemma 6 Let a in N
n+1
satisfy |a| = m. Then the number of x in N
m
such ... combinatorics 13 (2006), #N8 5
3 Start of the proof
Let N = {0, 1, }. Define the weight of a matrix N to be the sum of its entries, and
wri...
Báo cáo toán học: "On the number of subsequences with a given sum in a finite abelian grou" pptx
... g of G, the lower bound of N
g
(S) remains undetermined.
In this paper, we determine the best possible lower bound of N
g
(S) for an arbitrary
g of G. We also characterize the structures of the ... Tianjin 300071, P.R. China
5
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P.R. China
6
Department of Mathematics, Harbin University of Scienc...
Báo cáo toán học: " ON THE NUMBER OF DESCENDANTS AND ASCENDANTS IN RANDOM SEARCH TREES" ppsx
... +1)
6
49n
6
.
7. The number of ascendants of a given node in a LBST
As in the case of the number of ascendants in a random BST, computing the probability that
the j
th
node in a random LBST has ... JOURNAL OF COMBINATORICS 5 (1998), #R20 8
3. The number of descendants in random BSTs
The number of the descendants D
n,j
of the j
th
node of a...
Báo cáo toán học: "On the number of permutations admitting an m-th root" pptx
... 800 1000
Figure 1: The function m → κ
m
4.3. Statement and pro of of the main theorem
The situation is the following: we look for the asymptotics of the coefficients
p
n
(m) of the formal series ... is not the case. We approximate the c
n
(m) by the coefficients d
n
(m) of the expan-
sion in power series of the principal part D
m
of C
m
in a neighbourhoo...
Báo cáo toán học: " ON THE NUMBER OF FULLY PACKED LOOP CONFIGURATIONS WITH A FIXED" pot
... points of the planar integer lattice Z
2
,
such that for all i<jthe point A
i
is (weakly) south-east of the point A
j
, and the point
E
i
is (weakly) south-east of the point E
j
. Then the number ... every other horizontal edge in the region BCLK as indicated in the figure,
(4) the zig-zag lines in the corner regions above the line EA, respectively below...
Báo cáo toán học: "On the number of orthogonal systems in vector spaces over finite fields" ppsx
... o(1))
|E|
k
k!
q
−
(
k
2
)
,
completing the proof of Theorem 1.2.
Acknowledgments
The research is performed during the author’s visit at the Erwin Schr¨odinger International
Institute for Mathematical Physics. The author ... From (2.6) and (2.8), the number of copies of K
k
in E is
(1 + o(1))
|E|
k
k!
q
−
(
k
2
)
.
.
This implies that the number of the number...
Báo cáo toán học: "On the number of genus one labeled circle trees" doc
... E
1
is the intersection of {E
1
, E
2
,. . .,E
k+1
} and the points of one of the e-graphs, and point E
k+1
is the intersection of {E
1
, E
2
, . . . , E
k+1
} and the points of the other of the e-graphs.
Theorem ... K
1
and K
2
are identical. This can happen only
if
n−2
2
is even (since if K
1
and K
2
are identical, then the number of edges in K
1...
Báo cáo toán học: "On the Number of Planar Orientations with Prescribed Degrees" pptx
... is sandwiched between
that of G
2k−2,2−2
and that of G
2k,2
. Therefore the asymptotic behavior is the same and
in [24], the limit of the number of perfect matchings of G
2k,2
, denoted as Φ(2k, ... but using that we know the number
of edges exactly. Since in the independent set of the remaining face vertices all of them
have degree 4 and req...
Báo cáo toán học: "On the Number of Matchings in Regular Graphs" pptx
... its subset of bipartite graphs, we characterize the optimal graphs
who maximize and minimize the number of m -matchings.
We find the expected value of the number of m -matchings of r-regular bipar-
tite ... of m.
In the expression for φ(G, 4) the number of 4 -cycles appeared as the first structure in
the graph, apart from n and r, which affects the...