Báo cáo toán học: "Chromatically Unique Multibridge Graphs" potx
Báo cáo toán học: "ON RAMSEY MINIMAL GRAPHS" doc
... C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs for star
forests, Discrete Math. 33 (1981), 227–237.
[4] S.A.Burr, P.Erd˝os, R.J.Faudree, C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs for match-
ings,inThe ... Threshold functions for Ramsey properties,submitted.
Key words and phrases: critical graphs, Ramsey theory
1991 Mathematics Subject Classifications: 05D10, 05C80
4
O...
Báo cáo toán học: "Symmetry Breaking in Graphs" pptx
... and φ cannot be
distinguishing. This contradicts our assumption that φ is an r-distinguishing
labeling. ✷
We remark that this proves that the largest integer in D(S
3
)is3,since
the subgroups ... the goal is to minimize the number of colors used.
Consequently we define the distinguishing number of a graph G by
D(G)=min{r | G has a labeling that is r-distinguishing}.
The original key problem...
Báo cáo toán học: "Ramseyan Properties of Graphs by Ermelinda DeLaVina" doc
... the class of all 4-chromatic graphs.
The structure of the red graph is obvious by Corollary, but we do not know
which graphs can occur as blue graphs and what are the properties of graphs in
which ... on the Wall, a list of conjectures of Graffiti.
Ramseyan Properties of Graphs
by
Ermelinda DeLaVina
delavina@math.uh.edu
Siemion Fajtlowicz
siemion@math.uh.edu
Uni...
Báo cáo toán học: " Orthogonal Colorings of Graphs" ppt
... The notion of orthogonal colorings is strongly related to the
notion of orthogonal Latin squares. The orthogonal chromatic number of G, denoted by
Oχ(G), is the minimum possible number of colors ... 2, 3, 1, 3).
The notion of k -orthogonal colorings is strongly related to the notion of orthogonal Latin
squares. Recall that two Latin squares L
1
,L
2
of order r are...
Báo cáo toán học: "Nim-Regularity of Graphs" docx
... parts are all of size one.
Alternately, the complement of such a graph either has no edges or consists of the the
disjoint union of three or fewer complete graphs.
Proof. The complement of K
−
5
is ... similar proofs for complexes of
dimension 2 and higher. We conjecture that the answer is “yes,” but the complexity
of the proof would be astronomical, even for dimension 2. Hidden...
Báo cáo toán học: "Online Coloring Known Graphs" docx
... 68W25.
Keywords: graph coloring, online algorithms.
Abstract
The problem of online coloring an unknown graph is known to be hard.
Here we consider the problem of online coloring in the relaxed ... independence number α are known
in advance. The unknown case can be handled via a doubling technique, see [5].
Without loss of generality, α ≥ n/ log n.Letq =(1/2) log
n/α
n. Before colori...
Báo cáo toán học: "Constructions for cubic graphs with large girth" pdf
... shown
that cubic graphs with arbitrarily large girth exist (see Theorem 3.2) and so there
is a well-defined integer à
0
(g), the smallest number of vertices for which a cubic
graph with girth ... account of the problem of constructing cubic
graphs with large girth. There is a well-dened integer
à
0
(g), the smallest number of
vertices for which a cubic graph with gi...
Báo cáo toán học: "Chromatically Unique Multibridge Graphs" potx
... chromatically
unique if a
k
<a
1
+ a
2
, and find examples showing that θ(a
1
,a
2
, ···,a
k
)maynotbe
chromatically unique if a
k
= a
1
+ a
2
.
Keywords: Chromatic polynomials, χ -unique, χ-closed, ... θ(a
1
,a
2
, ···,a
k
) is χ -unique if a
i
≥ k − 1 for i =
1, 2, ···,k. ✷
Theorem 2.3 ([11]) Let h ≥ s +1≥ 2 or s = h +1. Then for k ≥ 5, θ(a
1
,a
2
, ···,a
k
)
is χ -unique if a
2
− 1...
Báo cáo toán học: "Weighted Aztec Diamond Graphs and the Weyl Character Formula" doc
... be the product
of the weights of all the edges in the matching. Then the weight of the Aztec graph A is
(A)=
m
(m), the sum over all matchings of A. Using the tilted version of the Aztec
diamond ... 1)-order Aztec diamond
subgraphs A
NW
, A
SW
,andA
SE
.LetA
mid
be the (n − 2)-order Aztec diamond subgraph
of A lying directly in the middle, concentric wi...
Báo cáo toán học: "Degree powers in graphs with forbidden subgraphs" docx
... ,
proving (8).
Inequality (9) follows easily, since, in fact, for every p>3, the function g (x)hasa
local minimum at 0. ✷
5 H-free graphs
In this section we are going to prove the following ... (5), we obtain that
(r −1)
n
p +1
+
2n
p +1
<n.
Letting n →∞, we see that p ≥ r, contradicting the assumption and completing the
proof. ✷
Maximizing independently each summand in...
Báo cáo toán học: "Distinguishing numbers for graphs and groups" docx
... |Γ|≤m! and the subset {y
1
, ,y
j
} satisfies
1. φ(y
i
)=i for each i,
2. y
i+1
is in Γ
i−1
.y
i
for each i from 2 to j − 1, and y
1
is in Γ
j−1
.y
j
,
then j ≤ m and |Γ
i−1
.y
i
|≥j − i + 2for each ... shows this and two
other graphs with the same automorphism group and demonstrates that all three have
different distinguishing numbers. This example disproves a conjecture in [...
Báo cáo toán học: "A note on graphs without short even cycles" pptx
... irregular graphs, Graphs and
Combinatorics 18 (2002), 53–57.
[2] N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, second
edition, 1993.
[3] J.A. Bondy, M. Simonovits, Cycles ... vine on P
∗
and P
∗
is the unique uv-geodesic.
Proof. Suppose, for a contradiction, that H is not a vine on P
∗
.Letx ≺ v be a vertex of
P
∗
at a maximum distance from u on P
∗
such th...
Báo cáo toán học: "Distinguishing infinite graphs" ppt
... |G| ≤ .
We note that an infinite locally finite graph can have infinite distinguishing number.
For a simple example consider the graph that is obtained from the one-way infinite path
v
0
, v
1
, ... the infinite case and find many similarities. We also determine
the distinguishing number of infinite hypercubes of arbitrary dimension.
To this end we take recourse to elementary results abo...
Báo cáo toán học: "Unit Rectangle Visibility Graphs" pptx
... past twenty years, rectangle visibility graphs have generated consider-
able interest, in part due to their applicability to VLSI chip design. Here we study
unit rectangle visibility graphs, ... 1985.
[13] T. Shermer. On rectangle visibility graphs II: k-hilly and maximum-degree 4.
Manuscript, 1996.
[14] T. Shermer. On rectangle visibility graphs III: external visibility and...
Báo cáo toán học: "The number of graphs not containing K3,3 as a minor" pptx
... Hence, the class of (maximal) planar graphs is contained in the class of maximal
K
3,3
-minor-free graphs and we can use the number of planar graphs and the number of
triangulations as lower bounds. ... preliminary version available at
http://algo.inria.fr/flajolet/Publications
[7] O. Gim´enez and M. Noy. The number of planar graphs and properties of random
planar...
Từ khóa: