Báo cáo toán học: "Asymptotically optimal tree-packings in regular graphs" pps
Báo cáo toán học: "Pan-factorial Property in Regular Graphs" pot
... 1-factor containing e,so
does G
∗
. By Theorem 1, G
∗
has a k-factor containing e and another k-factor avoiding e
for all k,1≤ k ≤ 2r − 1. Deleting the matching M from G
∗
,weobtaina[k, k + 1]-factor
the ... 1-factor F containing
e
and thus F is the 1-factor avoiding e.
the electronic journal of combina torics 12 (2005), #N23 2
Pan-factorial Property in Regular Graphs
∗
M. Kano
1
and Qi...
Báo cáo toán học: "Longest Induced Cycles in Circulant Graphs" pps
... maximum lengh of a cycle
in unit circulant graphs on a Dedekind domain quotiented by an ideal with r distinct
maximal factors. Dedekind domains are exactly those integral domains in which every
ideal ... of combinatorics 12 (2005), #R52 10
A Dedekind ring is simply a quotient of a Dedekind domain.
If R is a Dedekind domain, and m
i
is a maximal ideal of R,thenR/m
i
is a field and
thus cont...
Báo cáo toán học: " Degree constrained orientations in countable graphs" pps
... vertex v of in nite degree we can only demand all
or nothing. Setting u(v) to a finite value in Theorem 2 is the same as requiring in nitely
many outgoing edges at v, whereas putting u(v) = ∞ ... 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: "Asymptotically optimal tree-packings in regular graphs" pps
... t.
Proof. Partition the set of vertices V into t subsets V
1
,V
2
, ,V
t
by choosing for each
vertex randomly and independently an index i in {1, ,t} and placing it into V
i
.For
v ∈ V (G)and1≤ i ≤ t,letA
i,v
denote ... certain regularity and local density conditions on H,
one can find an almost perfect matching M in H, i.e., the number of vertices in no edge
of M is negligible. In fac...
Báo cáo toán học: "Asymptotically Optimal Box Packing Theorems" potx
... beginning
of the induction step follows along the same lines as the inductive proof of Theorem 3.1
given in [22], so one may even prove both theorems at once, inducting on the dimension.
In comparison, ... statement.
Determining the smallest value of C in the theorem is an interesting issue, but not
one that we will address here. Even in the 1-dimensional case, it is interesting; in...
Báo cáo toán học: "Asymptotically optimal pairing strategy for Tic-Tac-Toe with numerous directions" doc
... the pairing strategy to the new board.
As long as we do not chang e the length of the winning sets and the prescribed directions,
any winning set in the [N]
d
board is also a winning set in the ... for the latest in
generalization of Tic-Tac-Toe games, see [16]. Despite this, from a combinatorial point
of view, it still remains an interesting question to determine the best pairing strat...
Báo cáo toán học: "Multicoloured Hamilton cycles in random graphs; an anti-Ramsey threshold" pot
... endpoint in S, the other a distinct endpoint not in S and of a colour different
to that of any edge incident with a vertex of SMALL. This set of edges contains at least |M|/k
colours. If M contains ... P
1
.LetT
i
= {v ∈ C
1
: v = x is the endpoint of a path obtainable from P
1
by t rotations
with fixed endpoint x, pivot in int(C
1
) and all broken edges in P
1
}. We claim we can c...
Báo cáo toán học: "Minimal percolating sets in bootstrap percolation" pps
... that in Lemma 4, below, we need to use three extra
columns to ‘connect’ two corner-avoiding minimal percolating sets.
The next lemma explains our interest in corner-avoiding minimal percolating ... corner-avoiding minimal percolating
set. Then, using Lemma 5, we put about
√
m of these together to form a long thin
minimal percolating set with the right density. Finally we shall use Lemma 6...
Báo cáo toán học: "An extremal theorem in the hypercube" pps
... edge formed by replacing b
g(i
ℓ
)
in f(u) with a flip-bit is in G. But this edge is just the
edge between f(u) and f(v). We therefore have an embedding of H in G, completing the
proof. ✷
To complete ... chromatic number of H. In
particular, it is known [16] that ex(K
n
, H) = o(e(K
n
)) if and only if H is bipartite. In
this note, we will be similarly interested in determining sub...
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