... (the component
the electronic journal of combinatorics 13 (2006), #N14 5
2 Proof of the main theorem
By the recursive structure of rooted trees and the multiplicative properties of the cycle
index, ... related to the automorphism groups of
trees have been investigated. We state, for instance, the enumeration of identity trees
(see [7]), and the question of d...
... endpoint of one of his paths and
the electronic journal of combinatorics 16 (2009), #R28 12
Following [2], we define τ(H
n
) to be the minimum number of moves needed for Maker in
order to win H
n
(it ... K
n
which is induced on the vertices of B
k
(S). Let
G
k
(S) be the subgraph of G
k
(S) which is obtained by removing all edges (x, y) such that
x and y are endpoin...
... and there exist two induced paths in H
joining x and y one of which is of odd length at least 3 and the other of even length at
least 2.
Lemma 2.1: Let G be a 3-connected graph of girth five in ... .5(iii) there exist induced paths of length 3 and 4 joining x
i
and x
k
,
both avoiding x
j
.
Now arguing just as in the proof of Lemma 5.2, again we conclude that B...
... referee f or the careful reading, the help to
improve the exposition and the intriguing questions. We thank Ang´elica Benito for the
reading of the manuscript and her suggestions. The first author ... are a
version of the ‘shortcut’ mentioned in [4]. Before giving the actual definitions we motivate
them including here a very simple proof of Theorem 1.1 in a stron...
... ∗, se = k), where the ∗ indicates that there is no
the electronic journal of combinatorics 13 (2006), #N21 3
On the symmetry of the distribution of k-crossings
and k-nestings in graphs
Anna de ... c
k
) is
in the diagram.
We are interested in counting fillings where the sum of the entries is fixed. Let
N(F ; m; ne = k, se = l) be the number of arbitrary...
... levels r. Furthermore, the
variance of the channel capacity decreases by increasing the number of hops, while increase
in the severity of fading has an opposite in uence on the variance of the channel ... associated with the nth
link of the multihop communication system. Increasing the value of m
n
decreases the
severity of fading and vice versa. The o...
... > 0, and
φ(0) = 0 where . is any fixed norm on R
d
.
In recent years, there has been an increasing interest in the study of the asymptotic behavior of the
solutions of both convolution and non-convolution-type ... in general is non-trivial.
The main result on the boundedness of solutions of a linear Volterra difference system in [2] was improved
by Gy˝ori a...