Báo cáo toán hoc:" An Elementary Chromatic Reduction for Gain Graphs and Special Hyperplane" pps
Báo cáo toán hoc:" An Elementary Chromatic Reduction for Gain Graphs and Special Hyperplane" pps
... balanced, and we define the
chromatic and zero-free chromatic polynomials by means of (5.3) and (5.4).
Proposition 5.4. The total chromatic polynomial is a weak chromatic invariant of gain
graphs. ... Cat alan, Shi, and Linial graphs satisfy the hypotheses of Corollary 10.4 and
the graphs between Catalan and Shi are co mplete, it is a routine matter to evaluate their...
Báo cáo toán học: "An elementary proof of the hook formula" ppt
... present here
an elementary new proof which uses nothing more than the fundamental theorem
of algebra. This proof was suggested by a q, t-analog of the hook formula given
by Garsia and Tesler, and is ... the
proof given here. Thanks also is due to the National Science Foundation for support, and
to an anonymous reviewer for many useful suggestions.
3 A proof of the hook formula...
Báo cáo toán học: "An improved tableau criterion for Bruhat order" ppt
... <x
r
(for if
x
i,k
>x
k
then x
i−1,k−1
= x
i,k
and hence y
i−1,k−1
≤ y
i,k
<x
i,k
= x
i−1,k−1
which contradicts
An improved tableau criterion for Bruhat order
Anders Bj
¨
orner and Francesco ... Proctor [P] and for certain affine
Weyl groups by Bj¨orner and Brenti [BB] and by Eriksson and Eriksson [HE, EE].
In 1977 Deodhar [D] published a characterization of Bruhat...
Báo cáo toán học: " AN EXACT PERFORMANCE BOUND FOR AN O(m + n) TIME GREEDY MATCHING PROCEDURE" pptx
... of method (perhaps the greedy procedure) for handling dense
graphs, and another kind of method (perhaps an augmenting path algorithm) for
handling other graphs. It may be interesting to investigate ... increasing on [2,n], since f(r) and g(r) are. Also,
b(n, r) = max(f(n, r),g(n, r)) when n ≥ 2 and r ≥ 1. (7)
4 Performance Guarantees
The following performance guarantee for the...
Báo cáo toán học: " On the chromatic number of intersection graphs of convex sets in the plane" ppt
... A+u
(respectively,
V
= A + v
). Since U
and V
are between A and B, by Lemma 4, U
and V
intersect
V and each other. Let u
be the point on L
u
with the y-coordinate equal to y
v
and
U
= A + u
.SinceU
intersects ... if and only if they have common elements. Asplund and
Gr¨unbaum [3] and Gy´arf´as and Lehel [11, 9] started studying many interesting probl...
Báo cáo toán học: "An Ehrhart Series Formula For Reflexive Polytopes" pptx
... 1] and hence we get our result. This behavior can be generalized as follows:
Corollary 1 Suppose that P and Q are as in Theorem 1 and that {H
i
}
k
i=1
and {K
j
}
l
j=1
are halfspaces of the form ... Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces
in toric varieties. J. Algebraic Geom., 3(3):493–535, 1994.
[2] Matthias Beck and Serkan Ho¸sten. Cyclotomic polytope...
Báo cáo toán học: "On the chromatic number of simple triangle-free triple systems" pps
... t
u
= t
v
= t then c ∈ L
(t)
(w) and so κ(w) = c. If t
u
< t
v
= t then vw is an edge of G
(t)
and κ(vw) = c and so c ∈ L
(t)
(w) and again κ(w) = c.
6 Parameters for the problem
We will now ... (17)
Fix u and condition on the values γ
w
(c), η
w
(c) for all c ∈ C and all w /∈ N(u) and for
w = u. Now write u ∼ v to mean that there exists w such that uvw is an edge...
Báo cáo toán hoc:" An Edge-Minimization Problem for Regular Polygons " pps
... v}
and c
1
= c
2
such that
f
1
− c
1
g
1
= f
j
0
− c
1
g
j
0
and f
1
− c
2
g
1
= f
j
0
− c
2
g
j
0
.
Thus f
j
0
= f
1
and g
j
0
= g
1
, and (16) becomes (after swapping the indexes u + 1 and ... product
A(x)(1 + x
p
k
+ · · · + x
(p−1)p
k
) is expanded and collected with respect to x is ap, where a is
the number of terms in the expanded and collected form of A(x). Since these e...
Báo cáo toán học: "An Extremal Property of Tur´n Graphs a" potx
... = P
T
3
(6)
(4) = 96, and so this ends the
proof of Case 2, and of Theorem 1.
Acknowledgment
The authors are thankful to Sebastian Cioab˘a, Gary Ebert, and Qing Xiang for their
comments on ... [10], Read and Tutte [11],
Read and Royle [12], and recent preprints by Norine [9] and Zhao [16].
Let F
n,m
consist o f all (n, m) -graphs, that is, graphs of order n and size m. T...