Báo cáo toán học: "Extremal problems for t-partite and t-colorable hypergraphs" ppsx

... chromatic number of F is χ(F ) = min{t ≥ 1 : F is t-colorable} . Note that while a 2-graph is t-colorable iff it is t-partite this is no longer true for r ≥ 3, for example K (3) 4 is 2-colorable but not ... K (r) l+1 -free. the electronic journal of combinatorics 15 (2008), #R26 6 Extremal problems for t-partite and t-colorable hypergraphs Dhruv Mubayi ∗ John Talbot † Submit...

Ngày tải lên: 07/08/2014, 15:23

... consider the graph in which we delete u and w and clone v twice. That is, we form G  from G − u − w by adding vertices v  and v  joined to each other, v, and N G (v) \ {u, w}. Again, no independent ... previous notation and write i(G; ¯x) for the number of independent sets in G not containing x. Similarly, if G is a graph, and x and y are vertices of G, we write i(G; x, ¯...

Ngày tải lên: 08/08/2014, 14:23

... harmonic functions. We give also a Guelfond and Polya type theorem in the case of harmonic function. 2. Notations and Results For all z = re iθ ∈ C and n ∈ N we put: e 1 (z) ≡ 1,e n (z)=  r k cos ... Ma y 24, 2004 Abstract. For harmonic and separately harmonic functions, we give results similar to the Carlson-Boas theorem. We give also harmonic analogous of the Polya and Guelfo...

Ngày tải lên: 06/08/2014, 05:20

... the expansions for β(A) in terms of convex subsets generally have a simpler form than other expansions. In particular, the forms given for β(A) in Propositions 4.1, 4.2, 4.5, and 4.7 seem especially ... connectivity result for matroids (Theorem 7.3.2 of [28]): β(M)=0ifandonlyifM=M 1 ⊕M 2 (and M is not a loop). The converse of Proposition 2.3 is false for greedoids: It is possible...

Ngày tải lên: 07/08/2014, 06:20

... |Γ|≤m! and the subset {y 1 , ,y j } satisfies 1. φ(y i )=i for each i, 2. y i+1 is in Γ i−1 .y i for each i from 2 to j − 1, and y 1 is in Γ j−1 .y j , then j ≤ m and |Γ i−1 .y i |≥j − i + 2for each ... φ O and φ X\O . Consequently g is in the subgroup Stab(O) ∩ Stab(X\O)andsog is in Stab(X). This gives a numerical condition for 2-distinguishability. Corollary 2.4. Suppose Γ act...

Ngày tải lên: 07/08/2014, 08:20

... a merge of some α ∈ A and some β ∈ B} is also a permutation class, called the merge of A and B. For instance M(I s , I t ) = I s+t for any s and t. Let two permutations α and β be given, together ... 123789 and 456 and the type changes (6, 9) to (7, 4) b y position and (3, 3) to (7, 4) and (9, 6) to (4, 7) by value. Theorem 4. Let a positive integer B and two permutation...

Ngày tải lên: 08/08/2014, 12:22

... results for d = 2, k = 1, β 0 = 1, β 1 = 2, while item (ii) results for d = 2, k = 1, β 0 = 2, β 1 = 1. Moreover, upon setting k = 0 and β 0 = d + 1 in Theorem 2.2, we obta in Formula (1.2) (and ... inversion formula [8]. Finally, Section 4 is devoted to the proof of Theorem 2.2, and thus also of Theorem 1.2, which it generalises. 1.3 3-Coloured triangulations In the sequel, P n sta...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 15:20

... and the Tutte polynomial of a matroid. For more information on permutation groups, codes, and matroids, see [6, 10, 14] respectively. Let G be a permutation group on a set Ω, where |Ω| = n. For ... P. J. Cameron and D. G. Fon-Der-Flaass, Bases for permutation groups and matroids, Europ. J. Combinatorics 16 (1995), 537–544. [4] P. J. Cameron and D. E. Taylor, Stirling numbers...

Ngày tải lên: 07/08/2014, 06:23

... that g(n) f(n) < K ( g(n) f(n) > K) for a ll integers n and g(n) = Θ(f(n)) denotes the fa ct that both g(n) = O(f(n)) and g(n) = Ω(f(n)) hold. Throughout the paper log stands for the logarithm in the natural ... non-trivially intersecting hypergraph for a ll values of r and n. Here are the formal definitions. The Third Round Process Choose e 1 ∈  [n] r  uniformly at random....

Ngày tải lên: 08/08/2014, 12:22