Báo cáo toán học: "Toughness of Ka,t-minor-free graph" ppsx
Báo cáo toán học: "Toughness of Ka,t-minor-free graph" ppsx
... number of components
of G − S is (t − 1)(|S| − 2).
Proof. Let t = 2r + 1. Let H be a planar triangulation, and let n = |V (H)|. For each
face f of H, we add a set X
f
of r new vertices, each of which ... a path of length
2 log
l
n. B ondy and Locke [3] proved that, if a 3-connected graph has a path of length k,
then it has a cycle of length at least 2k/5. This easily completes...
Báo cáo toán học: "Kernels of Directed Graph Laplacians" potx
... number of reaches of G
M
equals the algebraic and geometric
multiplicity of 0 as an eigenvalue of M.
Proof. Let R
1
, , R
k
denote the reaches of G
M
and let H
i
denote the exclusive part of R
i
for ... 3
Proof. Let M = D − DS be given as stated. As in the proof of Theorem 3.2 above, we
may assume without loss of generality that
S
ii
= 1 whenever D
ii
=0. (2)
We further observ...
Báo cáo toán học: "Conjugacy of Coxeter elements" ppsx
... reduced form through a series of successive deletions of pairs of
letters (not necessarily adjacent). For uw
k
u
−1
, the number of such deletions is the
same as the number of letters in u. For any ... an equivalence relation on the set
of Coxeter elements, that corresponds precisely to the reacha bility relation on the set of
acyclic edge orientations.
Proof of theorem 1.1. O...
Báo cáo toán học: "Values of Domination Numbers of the Queen’s Graph" pdf
... All squares of column −59 and row 59 of Q
119
are
covered, so a copy of Q
118
is dominated.
the electronic journal of combinatorics 8 (2001), #R29 16
Values of
Domination Numbers
of the Queen’s ... squares of these orthogonals are not covered by the required lines
for a 0-cover D of size 2k + 1 for Q
4k+1
with e = f + 2; since the set of required lines of D
is symmetric ac...
Báo cáo toán học: "A Small Trivalent Graph of Girth 14" pot
... According to [1], this graph is the
smallest known trivalent graph of girth 14, improving the previous bound of 406 [2]. An
electronic copy of the adjacency list is available at
http://isu.indstate.edu/ge/CAGES/g3.14.384.
References
[1] ... for cubic graphs of large girth. Electron. J. Combin., 5 (1998)
A1.
[2] M. J. Hoare, On the girth of trivalent Cayley graphs. Graphs and Other C...
Báo cáo toán học: "Proof of an intersection theorem via graph homomorphisms" docx
... journal of combinatorics 13 (2006), #N6 1
References
[1] I. Dinur, S. Safra, On the importance of being biased (1.36 hardness of approximating
Vertex-Cover). Annals of Mathematics,toappear.Proc. of ... Thenµ
p
(I) ≤ p.
Our proof uses measure preserving homomorphisms between graphs.
One of the fundamental questions first studied in extremal graph theory is the question
of bounding...
Báo cáo toán học: "Evaluating a Weighted Graph Polynomial for Graphs of Bounded Tree-Width" potx
... block of either π
1
or π
2
must be in t he
same block of π. Hence the blocks of π are the blocks of π
1
∨ π
2
. Let B be a block of
π and for i = 1, 2 let w
i
(B) denote the number of vertices of ... definitions of tree-decompositions and of tree-width. A tree-decomposition
of a graph G = (V, E) is a pair
S = {S
i
|i ∈ I}, T = (I, F)
where S is a family of subsets
of...
Báo cáo toán học: "Application of graph combinatorics to rational identities of type A" ppt
... We
assume without loss of generality that C(e
0
) is admissible. Moreover,
e
0
∈ HE(C(e
0
)) ⇐⇒
The first dart of e
0
appears in
the tour of T before the second one.
Proof. The proof of the lemma, by ... denominator of the reduced
form of Ψ
P
is known (Bou07). In this article, the first author has investigated the effects
of elementary transformations of the Hasse diagram of a...
Báo cáo toán học: "Densities of Minor-Closed Graph Families" potx
... different type of minor of G. By induction on the
number of types of minors of G appearing in H, there is a densest minor of Fan(G, S, k)
of the form Fan(G
, S
, k) where G
is a minor of G. Among ... set of limiting densities of minor-closed graph families is the topological
closure of the set of densities of density-minimal graphs.
Proof. By Corollary 8, the se...
Báo cáo toán học: "Growth of graph powers" ppsx
... increase in the number of edges of the cube of a regular, co nnected graph.
Such an increase was already demonstrated by Hegarty in Theorem 2. Here we give an
alternative proof of that theorem, yielding ... diameter of G, diam(G), as the minimal
r such that G
r
is complete (alternatively, the maximal distance between two vertices).
Denote the number of edges of G by e(G). For v...