Báo cáo toán học: "k-Colour partitions of acyclic tournaments" ppt

... by  X k  the set of all k-subsets of X. A hypergraph H = (V ; E) is said to be k-uniform if E ⊂  V k  (the cardinality of any edge is equal to k). We shall always assume that the set of vertices V of a ... there exists a cyclic p α -partition of K (k) n . Section 2 contains the proofs of Theorems 1, 2 and 3 given below. Section 3 is de- voted to cyclic partitions of comp...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:21

... result of Kannan, Tetali and Vempala to com- pletely solve, via a simple proof, the problem of random generation of a labeled tournament with a given score vector. The proof uses the method of path ... score vector of a tournament is the sequence of out- degrees of the vertices of the tournament. In general, given a score vector with n scores, there can be an exponential (in n...

Ngày tải lên: 07/08/2014, 06:20

... class of cographs. 3 Spectrum of a cograph The characteristic polynomial ϕ(X) of the graph X is the characteristic polynomial of its adjacency matrix A(X). The spectrum of X is the collection of ... of eigenvalues of A(X), or equivalently, the collection of zeros of ϕ(X). The rank of X is the number of non-zero values occurring in the spectrum. In order to study the sp...

Ngày tải lên: 07/08/2014, 07:21

... yields the result that the absence of rainbow 5-cycles implies the absence of rainbow 9-cycles. Proof. The proof of this lemma has the same basic structure as that of Lemma 8, but the cycles we consider ... color of this chord. On the one hand, it must agree with one of the other edges of the n-cycle to avoid a rainbow n-cycle; on the other hand, it must similarly agree with one...

Ngày tải lên: 07/08/2014, 13:21

... and at least one of them contains an end of an edge of A  i ∩ B  since at least one of G[X i ∩ Y ] and G[X i ∩ Y ] contains an end of an edge of A i ∩ B. the electronic journal of combinatorics ... G ∗ is necessarily connected. Each bond of G is a circuit of G ∗ , and each circuit of G is a bond of G ∗ . If a theorem holds for a given set T of edges of G, then the...

Ngày tải lên: 08/08/2014, 11:20

... Introduction The score set S of a tournament T , a complete oriented graph, is the set of scores (outdegrees) of the vertices of T. In [5], Reid conjectured that each finite, nonempty set S of non-negative ... we give a new proof for the set of non-negative integers  s 1 , 2  i=1 s i , , p  i=1 s i  with s 1 <s 2 < ··· <s p to be the score set of some tourna- ment. T...

Ngày tải lên: 06/08/2014, 05:20

... ,k (9) Let B be the matrix of the coefficients of the (k +1)n + k equations (7)-(9). Lemma 11 Matrix B is of full row rank. Proof. We extend the first part of the proof of Lemma 6 to the case k>2. Each ... the matrix of the coefficients of the 4n + 1 equations (1)-(6). Lemma 6 Matrix A is of full row rank. Proof.Eacharc(j, n +1),j =0, ,n, of each of the two colours interfere...

Ngày tải lên: 07/08/2014, 08:22