Báo cáo toán học: "Splitting Numbers of Grids Dwight Duffus" pps
Báo cáo toán học: "Splitting Numbers of Grids Dwight Duffus" pps
... pleasing
characterization of these integer vectors. We do have a couple of observations about this
the electronic journal of combinatorics 12 (2005), #R17 29
Splitting Numbers of Grids
Dwight Duffus
Mathematics ... 1)y
k
+1.
This completes the proof of (7) and verification of the upper bound. The proof of
Theorem 1 is complete.
Note that, by (7) and the remark following the...
Báo cáo toán học: "Saturation Numbers of Books" ppsx
... set X of b − 1 vertices, each of degree n − 1, a clique L of
p
2
vertices, a
the electronic journal of combinatorics 15 (2008), #R118 7
Saturation Numbers of Books
Guantao Chen
∗
Dept. of Math. ... has a set X of b−1
vertices, each of degree n − 1, a clique L of
p
2
vertices, a set T of n − p/2 − b + 1 vertices
inducing an almost (p − 1)-regular graph which contains a ve...
Báo cáo toán học: "Fixing Numbers of Graphs and Groups" pptx
... examples of fixing sets of non-trivial finite groups are of the form {1, . . . , k }
for some k. If the fixing set of every non-trivial finite group is of this form, then the
computation of a fixing ... fix(Inf
k
(K
n
)) = ⌈
n−1
k+1
⌉.
Proof. The statement is clear for k = 0, so assume k > 0. Since each vertex of Inf
k
(K
n
)
is labeled with a sequence of the numbers {1, . . ....
Báo cáo toán học: "Betti numbers of monomial ideals and shifted skew shapes" potx
... Gale-
maximality of v to argue that if v lies in some face P of C
≤α
, then P ⊆ P
v,α
. We give this
argument explicitly below for only one of the five kinds of ideals, namely those of the form
I(F ... {b
3
} × {c
4
}.
Proof of Claim (b): If v is not the only vertex of C
≤α
, then because v is Gale-maximal,
without loss of generality we may assume that there is another vertex v...
Báo cáo toán học: "Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Riemann Surfaces" pot
... bounds on the isoperimetric numbers and bisection
widths of a large class of regular graphs of high degree. Our methods are com-
binatorial and do not require a knowledge of the eigenvalue spectrum. ... pieces A a nd B. The
isoperimetric number of a graph is a discrete version of the Cheeger constant of a manifold.
Upper bounds on the isoperimetric numbers of the Cayley gr...
Báo cáo toán học: "An extension of a criterion for unimodality" pps
... electronic journal of combinatorics 8 (2001), #R30 5
We now restate Theorem 2.2 in terms of the coefficients of P .
Theorem 2.3 Let 0 ≤ a
0
≤ a
1
···≤a
m
be a sequence of real numbers and n ∈ . ... similar.
the electronic journal of combinatorics 8 (2001), #R30 6
We begin by expressing the conditions on { a
j
} that guaranteed unimodality of P (x+1)
in terms of the coefficients {d...
Báo cáo toán học: "A Proof of the Two-path Conjecture" pps
... edge-disjoint union of two paths of length
n,wheren ≥ 2. Using a result of Thomason on decompositions of 4-regular graphs
into pairs of Hamiltonian cycles, we prove that G hasathirdpathoflengthn.
the ... An
H-decomposition of a graph G is a family of edge disjoint H–subgraphs of G whose union
is G.AnH-decomposable graph G is randomly H–decomposable if any edge disjoint
family...
Báo cáo toán học: "Parking functions of types A and B" ppsx
... r
n
into reflections of W
n
, its sequence of labels (l(r
1
), ,l(r
n
)), is a bijection from the set
of all factorizations to the set of type B parking functions.
For example the label of the factorization
(−1 ... the set of all such factorizations to the set of parking functions.
The above considerations show that this is just a rephrasing of Stanley’s Theorem
3.1. We shall g...
Báo cáo toán học: "A partition of connected graphs Gus Wiseman" pps
... ordering of the vertices
to an ordering of the edges lexicographically. A broken circuit of H ⊆ G is a set of edges
B ⊆ H such that there is some edge e ∈ G, smaller than every edge of B, such ... consists of all edges of G
with both ends in S.
We will use the symbols π and σ to denote set partitions. The notation π S means
π is a set partition of the set S. The length (numb...
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