Báo cáo toán học: "More Counterexamples to the Alon-Saks-Seymour and Rank-Coloring Conjectures" pps

... counterexamples to the Alon-Saks-Seymour Conjecture and to the Rank-Coloring Conjecture. We computed the eigenvalues of the adjacency matr ices of these graphs and obtained tight bounds for the ... fixed k ≥ 2 and r ≥ 1 and n larg e enough, the graphs G(n, k, r) are counterexamples to both the Alon-Saks-Seymour Conjecture and the Rank-Coloring Conjec...

Ngày tải lên: 08/08/2014, 12:23

Ngày tải lên: 05/08/2014, 15:21

... Haemers and Van Dam, [12] , and Garriga, Yebra, and the author [17] ,[18] ,[20] ,[21] , and also the recent theses of Van Dam [10] , Garriga [23] and Rodr´ıguez [37] . In their study, Garriga and the ... are trivial.) Then, by the converse of Theorem 2.5 , it must be Q k  u ≥ 1. On the other hand, in the proof of Theorem the electronic journal of combinatorics 4 (1...

Ngày tải lên: 07/08/2014, 06:20

... general introduction to complexity theory and detailed discussions of the polynomial time hierarchy and AM, we refer the reader to [9] and [4, 5]. The polynomial time hierarchy is the “polynomial ... now return to the first theorem advertised in the introduction, namely 1 Select a large rigid graph H and let G H be the graph formed by the disjoint union of K 3 an...

Ngày tải lên: 07/08/2014, 06:22

... 1997). the electronic journal of combinatorics 12 (2005), #R56 5 Asymptotics of generating the symmetric and alternating groups John D. Dixon School of Mathematics and Statistics Carleton University, Ottawa, ... that E(X)=expT (X)andso T (X)=logE(X). (1) We shall apply a theorem of Bender [2, Theorem 2] (quoted in [7, Theorem 7.3]): the electronic journal of combinatorics 12 (2005),...

Ngày tải lên: 07/08/2014, 13:21

... review the known identities such as the quintuple, sextuple and septuple products and establish several new theta function identities through Section 3 to 5 in the rest of the paper. 2 Main Theorem ... we state first the case β = 2 of Theorem 1 as follows. the electronic journal of combinatorics 14 (2007), #N7 6 For two indeterminate x and y with x = 0 and y = 0, there...

Ngày tải lên: 07/08/2014, 13:21

... Chen and Lin [2], Chen and Zame [3], Chen et al. [4], Guibas and Odlyzko [6], Li [7], Gerber and Li [5], and Mori [8]. In [3], Chen and Zame proved that for two-person games, public knowledge of the ... showed that if the string length is greater and equal to three, two players can collude to attain an advantage by choosing the pair of strings 11 . . . 10 and 00 . ....

Ngày tải lên: 08/08/2014, 01:20

... any k ≥ 1. By Theorem 1 , log-concavity provides an opportunity to show unimodality. In the proof of Theorem 5 we use it together with Theorem 2. the electronic journal of combinatorics 18 (2011), ... r). We a lso need a combinatorial argument to extend the Vandermonde identity  n ν  =  i  k i  n −k ν −i  linked to the Pascal triangle as follows. Theorem 4 Given the non...

Ngày tải lên: 08/08/2014, 14:23

... a r are the extremal points of Q(Δ). It suffices to show that every rational vector a ∈ Q(Δ) belongs to P (Δ). Let k be the least common multiple of the denominators of the components of a.ThenM T · ... combining Theorem 2.1 and Theorem 3.2 we obtain the following result of Gitler, Valencia and Villarreal [4, Theorem 3.5]. Corollary 3.1. Let I = I(Δ).ThenΔ is a Mengerian hyper...

Ngày tải lên: 06/08/2014, 05:20

... =0: ∅ the columns 1, ,2k from left to right and the rows 1, ,2k from bottom to top. Place an X in the box in column i and row j if and only if, in the one-row diagram of d, vertex i is the left ... is best suited to state and prove (1.4) and the Γ k notation is best suited to state and prove (1.5). The vacillating tableaux in [CDDSY] are the same as those i...

Ngày tải lên: 07/08/2014, 08:22