Báo cáo toán học: "Short cycles in random regular graphs" pps
Báo cáo toán học: "Short cycles in random regular graphs" pps
... short cycles in random regular graphs,
J. Combin. Theory, Ser. B 31 (1981) 168–182.
[11] N. C. Wormald, Models of random regular graphs. In J.D. Lamb and D.A. Preece
(eds.), Surveys in Combinatorics ... questions, the most “interesting” subgraphs are the cycles. For
this reason we consider only cycles in this paper. The girth of the graph is an interesting
property which...
Báo cáo toán học: "Component evolution in random intersection graphs" ppsx
... Component evolution in random intersection graphs
Michael Behrisch
∗
Institut f¨ur Informatik, Humboldt-Universit¨at zu Berlin, 10099 Berlin, Germany
behrisch@informatik.hu-berlin.de
Submitted: ... Colouring random intersection graphs and
complex networks. Preprint, December 2005.
[4] B. Bollob´as and O. Riordan. Slow emergence of the giant component in the growing
m-out graph. to app...
Báo cáo toán học: "Short Cycles in Digraphs with Local Average Outdegree at Least Two" pptx
... 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
vertex u
and ... n/2. Applying the above-
mentioned result, we improve their result by replacing the minimum outdegree con-
dition by some weaker conditions involving the local average outdegree. In...
Báo cáo toán học: "On cycles in the coprime graph of integers1" docx
... correspondance.
In this paper we are going to investigate another natural question of this type (also
initiated by the first author), namely what can we say about cycles in G(A). Thecaseof
even cycles ... from the following theorem in [9]: If n ≥ n
0
, |A
(2,1)
| = s>0, |A| >f(n, 1) and
r =min{s,
1
10
log log n},thenK(r, r) ⊂ G(A).
The case of odd cycles is more interestin...
Báo cáo toán học: "Consistent cycles in 1 -arc-transitive graphs 2" ppsx
... vertices in this
figure are arranged in three concentric rings, each inducing one of the six consistent 9-
cycles in the orbit. These three consistent cycles share the same shunt, being the rotation
of ... going between the rings induce the
other three consistent cycles in the orbit.
Now consider the drawing of the Doyle-Holt graph in Figure 2. Here the vertices
are arranged i...
Báo cáo toán học: "On Descents in Standard Young Tableaux" ppsx
... strings corresponding to some standard Young tableau of
shape λ beginning with some string w of length i − 1 followed by a, b and c in some order
and ending by some v. We may neglect the strings ... tableau also corresponds to a string of
numbers formed by reading the numbering in the order determined by the tableau. (This
has been called the inverse reading word of the tableau.) A standa...
Báo cáo toán học: "Induced paths in twin-free graphs" pptx
... vertices in graphs, IEEE Transactions on Information Theory, vol 44, pp.
599-611, 1998.
[6] A. Lobstein, Bibliography on identifying and locating-dominating codes in graphs,
http://www.infres.enst.fr/∼lobstein/debutBIBidetlocdom.pdf
[7] ... minimal
r-twin-free graph for the induced subgraph relationship. Indeed, we have:
the electronic journal of combinatorics 15 (2008), #N17 5
An r-twin-...
Báo cáo toán học: "nduced trees in triangle-free graphs" pdf
... Theorem 1.2 and it serves as an introduction
to it.
We begin with a lemma about selecting induced forests of a particular kind in a
bipartite graph. We introduce some terminology. Let H be a bipartite ... ··· ∪ M
induces a forest in G. We let T be the
component of this forest containing the single vertex of M
. Since every vertex of M
i−1
,
< i ≤ k, has at least one neighbor in...
Báo cáo toán học: "Heterochromatic matchings in edge-colored graphs" potx
... set of |T | distinct colors on some such set of |T | edges between S and distinct
vertices of T .
In [15], we obtained the following result concerning heterochromatic matchings in
colored bipartite ... partitioned into sets V
1
, · · · , V
r
in such a
way that each hyperedge meets each V
i
in precisely one vertex.
A matching in a hypergraph is a set of disjoint hyperedges. The match...
Báo cáo toán học: "Rainbow Matching in Edge-Colored Graphs" pot
... edges joining
u
j
to U have color λ
2
, and all edges joining v
j
to V have color λ
1
. If U and V are both
nonempty, then replacing u
j
v
j
with edges to each yields a larger rainbow matching in ... for K
4
or a graph obtained
from K
k+2
by removing a matching.
A survey on rainbow matchings and other rainbow subgraphs appears in [1]. Subgraphs
whose edges have distinct colors have also b...