Báo cáo toán học: "he spectral gap of random graphs with given expected degrees" pot
Báo cáo toán học: "he spectral gap of random graphs with given expected degrees" pot
... exp(−
¯
d
min
/(2C)),
the electronic journal of combinatorics 16 (2009), #R138 44
The spectral gap of random graphs with given
expected degrees
∗
Amin Coja-Oghlan
University of Edinburgh, School of Informatics
Crichton ... graphs with with given degree sequences.
Random Structures and Algorithms 32 (2008) 1–19
[7] Chung, F., Lu, L.: Connected components in rando...
Báo cáo toán học: "he spectral radius of subgraphs of regular graphs" ppt
... of G. If H is a component
of G − e with µ (H) = µ (G − e) , then
µ (G) − µ (H) >
1
Diam (H) |H|
.
This lemma follows easily from Theorem 2.1 of [2] and its proof is omitted.
Proofs
Proof of ... the proof. ✷
Proof of Theorem 3 Let x = (x
1
, . . . , x
n
) be an eigenvector to µ
min
(G) and let U =
{u : x
u
< 0} . Write H for the bipartite subgraph of G containing all edges...
Báo cáo toán học: "THE INDEPENDENCE NUMBER OF DENSE GRAPHS WITH LARGE ODD GIRTH" ppsx
... d
k−1
(v))
1+d
1
(v)+···+ d
k
(v)
.
Proof. Randomly label the vertices of G with a permutation of the integers from 1 to
n.LetA (respectively B) be the set of vertices v of G such that the minimum label ... 2
−
(
k−1
k
)
n
k−1
k
d
1
k
.
Proof. Immediate from Theorem 3.
This improves Denley’s Theorem 4.
References
1. Denley, T., The Independence number of graphs with large odd...
Báo cáo toán học: "The asymptotic number of set partitions with unequal block sizes" pot
... values of n, we shall use elementary estimates and some well-known bounds
for ordinary partitions (of a number) to express most values of b
n
in terms of the number
of ordinary partitions of k with ... the number of partitions of (the number) n,andQis its ordinary
generating function. Also, define p(n, k) to be the number of partitions of n with largest
part at most k. W...
Báo cáo toán học: "Multicoloured Hamilton cycles in random graphs; an anti-Ramsey threshold" pot
... between A and B.
Proof The proof follows that of Lemma 5. By P6, the number of edges between A and
B in G of a colour different to that of any edge incident with a vertex of SMALL is at least
M ... a growing literature
on the subject of the Ramsey properties of random graphs, see for example the paper of R¨odl and
Ruci´nski [17].
2 Outline of the proof of Theorem 1
We...
Báo cáo toán học: " LONGEST INCREASING SUBSEQUENCES OF RANDOM COLORED PERMUTATIONS" pps
... isomorphism of Proposition 5.1 we transfer our probability distribution
to the set of m–tuples of Young disgrams with total number of boxes equal to n.
Then by (5.2) we see that the probability of an ... correspondence
with pairs of 2–rim hook tableaux of the same shape with 2n boxes and width l.
The length of the longest increasing subsequence for signed permutations em...
Báo cáo toán học: "Minimal Cycle Bases of Outerplanar Graphs" ppsx
... (V
C
,C)ofG(V,E). The set C of all cycles forms a subspace of (E, ⊕, ·)
which is called the cycle space of G.AbasisBof the cycle space C is called a cycle
basis of G(V, E) [2]. The dimension of the ... number of its edges. The length (B) of a cycle
basis B is sum of the lengths of its cycles: (B)=
C∈B
|C|.Aminimal cycle basis
is a cycle basis with minimal length. Let c...
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