Báo cáo toán học: "Some gregarious cycle decompositions of complete equipartite graphs" ppsx
Báo cáo toán học: "Some gregarious cycle decompositions of complete equipartite graphs" ppsx
... pairs of cycles in such a way that the cycles in each pair share two adjacent edges .
Then there exists a gregarious k -cycle decomposition of G ∗ K
2
.
Proof Let D be a k -cycle decomposition of ... to
“nongregarious” cycle decompositions, few results are known. Of course 3 -cycle decom-
positions of complete equipartite graphs are necessarily gregarious and so by Han...
Báo cáo toán học: "Edge and total choosability of near-outerplanar graphs" ppsx
... 1, again contradicting the choice
of G. This completes the proof of Claim 3.1. ✷
In view of Claim 3.1 and Lemma 3.1, B must be K
4
-minor-free. By the proof of
Claim 2.1, B
∼
=
K
2
, so that ... vertices of degree
2, by Theorem 1.3. This contradiction completes the proof of Theorem 1.2. ✷
the electronic journal of combinatorics 13 (2006), #R98 6
Edge and total choosability of...
Báo cáo toán học: "Sharply transitive 1-factorizations of complete multipartite graphs" pot
... write
uniquely each element of H
i
as the sum of an element of K
1
i
together with an element
of K
2
i
, with K
1
i
a suitable subgroup of < d > and K
2
i
a suitable subgroup of < 2
m
>,
i.e., ... union of cycles. Namely: if the o r der
of h in G is t, then the cycles are given by (x, hx, h
2
x, . . . , h
t−1
x), as x varies in the set
of distinct representatives...
Báo cáo toán học: " Some geometric probability problems involving the Eulerian numbers" ppsx
... R
(n)
j+1
of [0, 1]
n
is partitioned, up to a set of
measure zero, by the images of the interiors of the simplices ∆
σ
for those signed permutations
satisfying des(σ) = j.
Proof. The former part of ... R
(n−1)
i
of ∆
n−1
is a projection of the section
S
(n)
i
of ∆
n
.
Proof. First, we describe the vertices of R
(n−1)
i
when i satisfies 2 ≤ i ≤ n −1. These vertices
fall into t...
Báo cáo toán học: "Minimum Weight H-Decompositions of Graphs: The Bipartite Cas" doc
... b)-decomposition
of G is a partition of the edge set of G such that each part is either a single edge or
forms an H-subgraph. We assign a weight of b to each H-subgraph in the decompo-
sition and a weight of ... part. We assign a weight of b to each H-subgraph in the
decomposition and a weight of 1 to single edges. The total weig ht of the deco mposition
is the sum of the we...
Báo cáo toán học: " A Blowing-up Characterization of Pseudo Buchsbaum Modules" ppsx
... second statement of Theorem 1.
ProofofStatement(ii) of Theorem 1. By the same argument in the proof of
Stament (i) of Theorem 1, we can assume without loss of generality that A is
complete.
Assume ... ideal of M
and let (x
1
, ,x
d
) be a system of
parameters of M
such that q
=(x
1
, ,x
d
)A. Then the lemma is proved if we
can show the existence of a system of para...
Báo cáo toán học: "The Strongly Regular (40, 12, 2, 4) Graphs" ppsx
... types:
1. a 12 -cycle,
2. the disjoint union of a 9 -cycle and a triangle,
3. the disjoint union of two 6-cycles,
4. the disjoint union of a 6 -cycle and two triangles,
5. the disjoint union of four triangles.
One ... each pair of non-
adjacent neighbours has 4 common neighbours. In [3] an incomplete enumeration of
strongly regular (40, 12, 2, 4) graphs established the existenc...
Báo cáo toán học: "Minimum connected dominating sets of random cubic graphs" docx
... the next operation of Type i.
We proceed with an examination of each of the two phases before giving a formal
definition of the distinction between the phases. For a clutch of operations in each ... least to within an additive
constant, of the main result of [10]. They also showed that the size of a connected
dominating set of an n-vertex cubic graph of girth at least 5 is...
Báo cáo toán học: "A prolific construction of strongly regular graphs with the n-e.c. property" pptx
... most of
the graphs generated have the n-e.c. property in Section 4, thereby completing the proof
of Theorem 1.1. The proof of the n-e.c. property uses bounds on the expected number of
pairs of ... characters as in the proof of Theorem 10, Section XIII.2,
of Bollob´as [2]. If U and W are disjoint sets of vertices of the Paley tournament
→
P
q
,then
we denote by v(U, W ) the n...
Báo cáo toán học: " Neighbour-distinguishing edge colourings of random regular graphs" ppt
... replacements
α α
α
α
γ
γ
γ
γ
γ
β
β
β
β
Figure 1: The colouring of H used in the second case of the proof of Lemma 1 when n ≡ 1
(mod 3)
3.2 Proof of Lemma 1
Fix d ≥ 5, n ≥ 6, and let G be a (d − 2)-regular ... deferred to Section 4.
the electronic journal of combinatorics 13 (2006), #R77 2
Let us see now how these two lemmas yield the proof of Theorem 2.
Proof of Theorem 2. Note...
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