Báo cáo toán học: "Rainbow matchings in properly edge colored graphs" pps
Báo cáo toán học: "Rainbow matchings in properly edge colored graphs" pps
... rainbow if its edges have distinct colors. Recently rainbow subgraphs have received
much attention, see the survey paper [8]. Here we are interested in rainbow matchings.
The study of rainbow matchings ... 05C15, 05C70
Abstract
Let G be a properly edge colored graph. A rainbow matching of G is a matching
in which no two edges have the same color. Let δ denote the minimum degree...
Báo cáo toán hoc:" Rainbow matchings in r-partite r-graphs" pps
... two of which sharing
an edge, h as an s -colored t-matching contained in its union.
In the case r = 2 the conjecture is that a set of t+1 disjoint t -matchings has a t-rainbow
matching. This is yet ... that there exists in H
′
a matching M of V
1
, containing the
edge (x, y, z). Color all edges in M by color 1, and for every edge a = (p, q, r) colored
1 by f, if there exists...
Báo cáo toán học: "Perfect Matchings in Claw-free Cubic Graphs" pdf
... one of the edges
incident with x will be a cutedge of G, a contradiction.
Thus u and v are nonadjacent in G. Let G
′
= (G \ D) + uv, that is obtained from
G by deleting D a nd adding an edge uv. ... with only 9 perfect matchings
We prove that every claw-free cubic n-vertex graph with no cutedge has more than
2
n/12
perfect matchings. The graph should not have any cutedge; in Figure 1...
Báo cáo toán học: "On domination in 2-connected cubic graphs" pps
... graph G containing F
i
and any dominating set D in G, the set
D has at least 9 vertices in V (F
i
).
If D contains neither x
i
nor y
i
, then by Claim 1 D must contain 3 vertices in each of
V ... bound was proved in [2] by exploiting Reed’s techniques
in [9] and examining some of the cases in Reed’s proof more carefully and adding a dis-
charging argument. However, exploting Reed’...
Báo cáo toán học: "Colorful Paths in Vertex Coloring of Graphs" pps
... χ(G). Since there are no good
cycles in G, therefore the coloring of V ( G )\S is proper. For each w ∈ Q\S, there is a
w-colorful path in V (G)\S going downward in T t hro ugh P , by passing from ... child in P. For each w ∈ V (G)\Q, there is a w-colorful path in V (G)\S going
upward in T by passing from each vertex to its parent.
So for each w ∈ V (G)\S, there is a w-colorful pat...
Báo cáo toán học: "Perfect matchings in -regular graphs" potx
... +2)
n
n!.
Thus, the number of perfect matchings in any super (d, )-regular graph on 2n vertices
is close to the expected number of such matchings in a random bipartite graph with
edge probability d (which ... 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...
Báo cáo toán học: "Maximum matchings in regular graphs of high girth" ppt
... The set of incidence vectors of the matchings of G have a
convex hull which is equal to the polytope containing all x ∈ R
E
which satisfy the following
the electronic journal of combinatorics ... matching (or one-factor) of G is a subgraph of G in which each vertex has
degree at most one. A basic question in combinatorial optimization is, “What is the size of a
maximum matching in a g...
Báo cáo toán học: "Heterochromatic matchings in edge-colored graphs" potx
... heterochromatic matchings in edge-
colored bipartite graphs, to appear in Ars Combinatoria, 2006.
[15] H. Li and G.H. Wang, Color degree and heterochromatic matchings in edge- colored
bipartite ... 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...
Báo cáo toán học: "Rainbow Matching in Edge-Colored Graphs" pot
... is odd, every proper n -edge- coloring of the complete bipartite
graph K
n,n
contains a rainbow perfect matching.
Wang and Li [4] studied rainbow matchings in arbitrary edge- colored graphs. We use
the ... all 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 ra...
Báo cáo toán học: "Monotonic subsequences in dimensions higher than one" ppsx
... ,thenany
point z
j
lies inside the triangle determined by the preceding three points in this
ordering.
To start the induction, for k =1wechoosez
1
to be a point, for k =2letz
1
and
z
2
be any two distinct ... the distri-
bution of longest increasing subsequences in random permutations, in
preparation.
[11] A. M. Odlyzko and E. M. Rains, On longest increasing subsequences
in random per...