Báo cáo toán học: "Degree powers in graphs with forbidden subgraphs" docx
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 hoc:"Degree powers in graphs with a forbidden even cycle" pdf
... e
G
(X) for the number of edges induced by X;
- e
G
(X, Y ) for the number of edges joining vertices in X to vertices in Y ;
- G −u for the graph obtained by removing the vertex u ∈ V (G) ;
- Γ
G
(u) ... graph G − u into the sets
A = Γ
G
(u) and B = V (G) \(Γ
G
(u) ∪ {u}) . Since G contains no C
2k+ 2
, the graph G −u
does not contain a path of order 2k + 1 with both ends in A. Applyi...
Báo cáo toán học: "Degree distributions in general random intersection graphs" pptx
... Computing, 8:131–
159, 1999.
[10] A. N. Lager˚as, M. Lindholm, A note on the component structure in random inter-
section graphs with tunable clustering. The Electronic Journal of Combinatorics, ... 10]. A generalized random
intersection graph is introduced in [5] by allowing a more general connection probability
in the underlying bipartite graph. The corresponding vertex degrees ar...
Báo cáo toán học: "Symmetry Breaking in Graphs" pptx
... by analyzing the
stabilizers of the possible orbits and providing 2-distinguishing colorings for
graphs with 6-orbits, and graphs without 6-orbits, but with 3-orbits. Clearly
graphs with largest ... the original, and the original labeling is
r-distinguishing if and only if the new graph is rigid.
Although a given group might be the automorphism group of graphs with
different di...
Báo cáo toán học: "Constructions for cubic graphs with large girth" pdf
... When g = 6 the minimal cubic graph is Heawood’s graph with 14
vertices. (It is the incidence graph of points and lines in the seven point projective
plane.) Excising a tree consisting of a vertex ... that constructing Cayley
graphs that have triangles, and then collapsing the triangles, can lead to graphs
with large girth. Using this ‘collapsing method’ they obtain a graph with 80...
Báo cáo toán học: "Short Cycles in Digraphs with Local Average Outdegree at Least Two" pptx
... minimal digraphs with given girth, Proc. 9th S-E
Conf. Combinatorics, Graph Theory and Computing (1978), 181-187.
[5] V. Chv´atal and E. Szemer´edi, Short cycles in directed graphs, J. Combin. ... deg
+
(u)+deg
+
(v) ≥ 3 for all
pairs of distinct vertices u, v in G,theng ≤n/2.
2 Main Results
Suppose u is a vertex in G. If a digraph G
is obtained from G by adding to it an extra
ve...
Báo cáo toán hoc:" Defective choosability of graphs without small minors" docx
... P
2
, P
3
connecting two vertices a, b, and
suppo se that u is in P
1
. The remaining vertices of P
1
(including a and b) can easily be
coloured with no bad edges. Colour the internal vertices ... a
n−1
we obtain K
5
− e as a minor, which is again a co ntradiction.
So supp ose that G does not contain such a path P . Then, applying Claim 2 with
H = W
n
, G has no minor formed as in Cla...
Báo cáo toán học: " Degree constrained orientations in countable graphs" pps
... we
add the centre c to L we do not gain any new edges since every edge is already incident
with a leaf but since l(c) > 0 the demand for ingoing edges increases. Hence, L ∪ {c} has
negative ... the in nite star. We immediately encounter the problem
that the set L of all leaves is incident with in nitely many edges but has in nite demand
for ingoing edges, i.e. l(L) = ∞. This results...
Báo cáo toán học: "Perfect matchings in -regular graphs" potx
... bound
follows by applying the Stirling approximation formula for factorials.
It is worth noting that since every -regular graph with density d and 2n vertices
contains, in each color class, at ... M. D. Plummer, Matching Theory, Akad´emiai Kiad´o, Budapest,
1986
[6] H. Minc, Nonnegative Matrices, Wiley, 1988
[7] V. R¨odl and A. Ruci´nski, Perfect matchings in -regular graphs and the...
Báo cáo toán học: "Short cycles in random regular graphs" pps
... distributed as independent Poisson variables with means (d − 1)
r
/2r,provided
d ≤
√
2logn − 1withg fixed (and independently in [10] for fixed d). In this paper we
allow d = d(n)andg = g(n)toincreasewithn, ... combinatorics 11 (2004), #R66 12
Theorem 3 For any d and n such that N(n, d) =0,letJ ⊆ E(K
n
). Then, with [x]
m
denoting the falling factorial and j
i
the number of edges in J...
Từ khóa: