Abstract: A graph G is fractional k-covered if for each edge e of
G, there exists a fractional k-factor h, such that h(e) = 1. If k = 2,
then a fractional k-covered graph is called a fractional 2-covered
graph. The binding number bind(G) is defined as follows,
bind(G) = min{|NG(X)|
|X|
: ├ÿ = X Ôèå V (G),NG(X) = V (G)}.
In this paper, it is proved that G is fractional 2-covered if δ(G) ≥ 4
and bind(G) > 5
3 .
Abstract: Let a and b be nonnegative integers with 2 ≤ a < b, and
let G be a Hamiltonian graph of order n with n ≥ (a+b−4)(a+b−2)
b−2 .
An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F
contains a Hamiltonian cycle. In this paper, it is proved that G has a
Hamiltonian [a, b]-factor if |NG(X)| > (a−1)n+|X|−1
a+b−3 for every nonempty
independent subset X of V (G) and δ(G) > (a−1)n+a+b−4
a+b−3 .
Abstract: The information systems with incomplete attribute
values and fuzzy decisions commonly exist in practical problems. On
the base of the notion of variable precision rough set model for
incomplete information system and the rough set model for
incomplete and fuzzy decision information system, the variable rough
set model for incomplete and fuzzy decision information system is
constructed, which is the generalization of the variable precision
rough set model for incomplete information system and that of rough
set model for incomplete and fuzzy decision information system. The
knowledge reduction and heuristic algorithm, built on the method and
theory of precision reduction, are proposed.
Abstract: Six Sigma is a well known discipline that reduces
variation using complex statistical tools and the DMAIC model. By
integrating Goldratts-s Theory of Constraints, the Five Focusing
Points and System Thinking tools, Six Sigma projects can be selected
where it can cause more impact in the company. This research
defines an integrated model of six sigma and constraint management
that shows a step-by-step guide using the original methodologies
from each discipline and is evaluated in a case study from the
production line of a Automobile engine monoblock V8, resulting in
an increase in the line capacity from 18.7 pieces per hour to 22.4
pieces per hour, a reduction of 60% of Work-In-Process and a
variation decrease of 0.73%.
Abstract: Let G be a Hamiltonian graph. A factor F of G is called
a Hamiltonian factor if F contains a Hamiltonian cycle. In this paper,
two sufficient conditions are given, which are two neighborhood
conditions for a Hamiltonian graph G to have a Hamiltonian factor.
Abstract: Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.
Abstract: Let G be a graph of order n, and let a, b and m be positive integers with 1 ≤ a n + a + b − 2 √bn+ 1, then for any subgraph H of G with m edges, G has an [a, b]-factor F such that E(H)∩ E(F) = ∅. This result is an extension of thatof Egawa [2].
Abstract: Let G be a graph of order n, and let k 2 and m 0 be two integers. Let h : E(G) [0, 1] be a function. If e∋x h(e) = k holds for each x V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G) k + m + m k+1 , n 4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)} n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.