Báo cáo toán hoc:"Tetravalent non-normal Cayley graphs of order 4p" ppsx
Báo cáo toán hoc:"Tetravalent non-normal Cayley graphs of order 4p" ppsx
... non-normal Cayley graphs of order 4p are
constructed explicitly for each pr ime p. As a result, there are fifteen sporadic and
eleven infinite families of tetravalent non-normal Cayley graphs of ... tetravalent non-normal Cayley graphs of order
4p with p a prime. It appears that there are fifteen sporadic and eleven infinite families of
tetravalent no n-normal Cay...
Báo cáo toán học: "Integral Quartic Cayley Graphs on Abelian Groups" pdf
... Suppose
all of the elements of S are of order two. Then |G| = 8 or 16. Otherwise since S = S
−1
and 1 /∈ S, the proof falls naturally into two parts.
i) There are exactly two elements of order two ... C
6
) = Γ
12
. Hence all of the connected,
regular integral graphs up to seven vertices are Cayley graphs. In other words there are
exactly 12 connected, integral Cayley gr...
Báo cáo toán học: "Bounding the partition function of spin-systems" ppsx
... vertices of G of the weights of the spins times the product over the edges
of G of the weights of the spin-pairs. In this language Z
W
(G) is the partition function of the
the electronic journal of ... tight in the
case of a family of graphs satisfying βd = ω(1).
We give the proof ofTheorem 1.3in Section 3. An important tool in theproof is an extension
of Theorem 1.1 t...
Báo cáo toán học: "Derangement Polynomials and Excedances of Type B" ppsx
... extension
of the decomposition of derangements given by Kim and Zeng [11] in their combinatorial
proof of (1.3).
Combinatorial Proof of Theorem 3.3. First, we give an outline of the proof of Kim ... sequence.
The proof turns out to be an application of the following theorem of Zhang [18].
the electronic journal of combinatorics 16(2) (2009), #R15 9
It follows that the number...
Báo cáo toán học: "Growth rates for subclasses of Av(321)" ppsx
... each element of λ
i
is labeled with the largest label of an element of
λ
i−1
of smaller value.
• For odd i > 1, each element of λ
i
is labeled with the largest label of an element of
λ
i−1
to ... articulation
points to any or all of the other patterns. The method of proof is to s how that the
elements of the latter classes can be represented as bounded merges of eleme...
Báo cáo toán học: "ON RAMSEY MINIMAL GRAPHS" doc
... least
n(log n)
2
edge-disjoint copies of G and the first part of the assertion follows.
In order to verify (b) let Y denote the number of subgraphs of G(n, p)ofsizes, s ≤ r,
with more than (s − ... matching.
ProofofTheorem1. We shall deduce Theorem 1 from the following lemma, a prob-
abilistic proof of which we postpone until the next section. Here and below, we denote by
V (G)andE...
Báo cáo toán học: "Symmetry Breaking in Graphs" pptx
... orbit of G hassizelessthanorequalto5.
By Lemma 2, we may assume that the stabilizer of every vertex is one of
the second two types: either <σ
j
,τσ
i
> of order
2n
j
or <τσ
i
> of order
2. ... 2-coloring the edges of K
n
we can break every vertex automorphism
of K
n
, since every automorphism of the vertices of K
n
is an automorphism
of the edges as well. L...
Báo cáo toán học: "Online Coloring Known Graphs" docx
... vertex.
Proof. Consider a vertex presented from block i,andletH be the hue of the bin
used. By the definition of the edges of the graph, H must be a subset of C
i
. Further,
H must also be a subset of ... game of Section 1.
Let [k]={1, 2, 3, ,k} denote the set of colors used by the adversary, and [k]
t
denote the collection of all t-element subsets of [k].
1. Alice announces...
Báo cáo toán học: "A Quasi-Spectral Characterization of Strongly Distance-Regular Graphs" ppsx
... strongly-regular graphs
among regular graphs, and study some of its consequences.
Given any vertex u of a graph with diameter d,wedenotebyN
i
(u), 0 ≤ i ≤ d,
the i-neighbourhood of u, or set of vertices ... regular graphs (i.e. d = 2), all the antipodal distance-
regular graphs, and some distance-regular graphs with diameter d =3. The
main result in this paper is a characteriz...