Báo cáo toán học: "Asymptotically optimal tree-packings in regular graphs" pps

... 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...

Ngày tải lên: 07/08/2014, 08:22

... 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...

Ngày tải lên: 07/08/2014, 13:21

... 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...

Ngày tải lên: 07/08/2014, 21:20

... 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...

Ngày tải lên: 07/08/2014, 06:22

... 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...

Ngày tải lên: 07/08/2014, 21:20

... 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...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 15:20

... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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...

Ngày tải lên: 07/08/2014, 21:21

... 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...

Ngày tải lên: 08/08/2014, 12:22