Báo cáo toán học: "Perfect matchings in -regular graphs" potx
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 ... and 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 a...
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 ... n < 2n
0
(d, g).
1 Introduction
For a graph G, a 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...
Báo cáo toán học: "Perfect Matchings in Claw-free Cubic Graphs" pdf
... e
3
will be incident with
v
1
, v
2
, v
3
respectively.
Every ver tex in a claw-free cubic graph is in 1, 2, or 3 triangles. If a vertex is in 3
triangles, then the component containing the vertex ... permanents of certain (0, 1)-matrices. Nederl.
Aka d. Wetensch. Ind ag. Math., 41(1):83– 86, 1979.
the electronic journal of combinatorics 18 (2011), #P62 6
Perfect Matchings in Claw-f...
Báo cáo toán học: "Extension of Strongly Regular Graphs" potx
... Spence [11].
In this paper, we yet introduce another extension of strongly regular graphs, from a
different direction. In 1966, Erd˝os, R´enyi, and S´os [1, 4] proved the following interesting
result, ... vertices u, v in V
i
(i = 1, 2), then by Claim 2, µ = δ(u, v) ≥ |V
3−i
| ≥ 2,
contradicting µ = 1. Thus there is no pair of non-adjacent vertices in each V
i
. By Claim
2, G = K
n
, c...
Báo cáo toán học: "Irregularity strength of regular graphs" potx
... for bringing the
main problem of this paper to my attention during an interesting discussion in Budapest,
and to Ingo Schiermeyer for his help and remarks in Freiberg. I also enclose greetings ... the domination number of G, γ(G), which is
the size of the smallest dominating set of G, i.e. the subset, say D, of V (G) such that
each vertex in V (G) D has a neighbour in D. The followi...
Báo cáo toán học: "On k-Walk-Regular Graphs" potx
... Thus,
a 0-walk-regular graph is the same concept as a walk-regular graph. In the other ex-
treme, the distance-regular g r aphs correspond to the case of D-walk-regular gr aphs (see
e.g. Rowlinson [11]). ... paper we introduce a generalization of bo th
distance-regularity and walk-regularity, which we call k-walk-regularity. In particular, we
present some algebraic characterizations of k-...
Báo cáo toán học: "Perfect codes in Cartesian products of 2-paths and infinite paths" pptx
... [2]).
In [1], Biggs introduced perfect codes in graphs. From this point of view, a perfect
binary single-error correcting code of length k is a perfect code on the hypercube Q
k
,and
a tiling of ... in nite length. Both existence and nonexistence
results are given.
1 Introduction
Perfect codes appeared in error correcting codes theory during the late 40’s with the
work of Golay and Ham...
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 ... The 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 edg...
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 ... similar, with one main difference: instead of
leaving each matching M
i
after o ne edge, we continue choosing edges from it, until all
edges in some matching M
j
represented in K have ap...
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 ... then G has
a rainbow matchin g of size at least ⌊
2δ
3
⌋.
Keywords: rainbow matchings, properly colored graphs, triangle-free graphs
1 Introduction and notation
We use [3] for termin...