Báo cáo toán học: "Graph Theory for Metric Dimension and Diameter" docx
Báo cáo toán học: "Graph Theory for Metric Dimension and Diameter" docx
... cardinality is a metric basis of
G, and |S| is the metric dimension of G, denoted by β(G).
For positive integers β and D, let G
β,D
be the class of connected graphs with metric
dimension β and diameter ... 20
Extremal Graph Theory for
Metric Dimension and Diameter
∗
Carmen Hernando
†
Departament de Matem`atica Aplicada I
Universitat Polit`ecnica de Catalunya
Barcel...
Báo cáo toán học: "Rook Theory, Generalized Stirling Numbers and (p, q)-analogues" docx
... 0 and t − 1 exactly once for each e
t
≤ i and lb
t
takes on each
value between 1 and t − 1 exactly once for each e
t
>i. We list the values of r
t
in increasing
order first for e
t
=0,nextfore
t
= ... K. Briggs and J. B. Remmel, A rook theory model for the p, q-analogues of Hsu and
Shuiue’s Generalized Stirling Numbers, in preparation.
[9] M. Dworkin, An interpretation...
Báo cáo toán học: "RSK Insertion for Set Partitions and Diagram Algebras" pps
... of a standard tableaux T
λ
of shape
λ and vacillating tableaux P
λ
of shape λ and length 2k for some λ ∈ Λ
k
n
. Our bijection
uses jeu de taquin and RSK column insertion.
If T is a standard ... Dulucq and Sagan [DS]
extend this insertion to work for partial matchings (and other generalizations for skew
oscillating tableaux) and Roby [Ry2] shows that the growth diagrams also...
Báo cáo toán học: "Extremal problems for t-partite and t-colorable hypergraphs" ppsx
... x
j
= 0 for some j ∈ {1, 2, . . . , t}. Let a
k
= |V
k
|, a
j
= |V
j
|
and = x
k
a
j
a
k
/(a
j
+ a
k
). Define a new weighting x
by x
v
= x
v
for v ∈ V \(V
k
∪ V
j
),
x
v
= /a
j
for v ... x
v
for v ∈ V \(V
k
∪ V
j
),
x
v
= /a
j
for v ∈ V
j
and x
v
= x
k
− /a
k
for v ∈ V
k
. It is straightforward to check that
x
∈ S
p
and λ(G, x
) > λ(G, x), co...
Báo cáo toán học: "Entrywise Bounds for Eigenvectors of Random Graphs" docx
... notation, the basic Random graph model and statement
of the result for Random gra phs. In Section 3 we present two proofs. Section 4 shows
that out bound is tight for quasi-random graphs. In Section ... Lemmas 10 and 11, respec-
tively. For these lemmas, we assume v(1) = v
min
= b > 0 and define S
t
and n
t
analogously:
• S
1
= {1}
• S
t+1
= {i : i ∈ N(S
t
) and v(i) b(1 +...
Báo cáo toán học: "Discrepancy of Matrices of Zeros and Ones" docx
... minimum discrepancy problem by giving an explicit for-
mula in terms of R and S for it. On the other hand, the problem of finding an
explicit formula for the maximum discrepancy turns out to be very ... the following:
1. Region i is connected for each i =1, 2, and
2. The intersection of each row of A with region i is connected for each i =1, 2,
and define, for each A ∈A(R, S),...