Báo cáo toán học: "The Loebl–Koml´s–S´s conjecture for trees of o o diameter 5 and for certain caterpillars" pptx

... all trees of diameter 4. Our main result is a proof of Conjecture 1 for all trees of diameter at most 5. Theorem 2. Let k, n ∈ N, and let G be a graph of order n so that at least n/2 vertices of ... subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey n...

Ngày tải lên: 07/08/2014, 21:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

... Think of the columns of the array (1) as wooden playing pieces, like dominoes. If we scan one of the pieces from top to bottom we see a block of 0 or more 1’s and 2’s followed by a block of 3’s and ... and take C to be one of the diagonal blocks of Λ m other than the first or last block. Certainly the hypotheses of the lemma hold, so no eigenvalue of C can exceed m + 1...

Ngày tải lên: 07/08/2014, 06:20

... southeast corners of the components of the diagram. The essential set E(w)ofapermutationw is defined to be the set of white corners of the diagram of w. For every white corner (i, j)ofw,itsrank ... 1)! Proof We will prove the proposition by induction on n. It is trivially true for n =2. Given a permutation matrix w ∈ S n , we remove the first row and the column of the dot in t...

Ngày tải lên: 07/08/2014, 06:20

... just need to switch the above formulas. This completes the proof of statements 2 and 3 of Theorem 4 .5. We now turn to statement 4 of Lemma 4.7 and statements 4 and 5 of Theorem 4 .5. For the lemma, ... the coefficients grow without bound as c − b becomes large. The first author examines this phenomenon in the special case of two-row shapes in [7]. We now turn to the proof...

Ngày tải lên: 07/08/2014, 08:20

... Union-Closed Sets Conjecture. Ars Combin. 49 (1998), pp. 280-288. [2] K. Henry and M. S. Roddy, A Notion of Reducibility for Union-Closed Families of Sets. (in preparation) [3] R. T. Johnson and ... set from level l of C which is in F, at most u of its subsets from level k could be in F, and for every set from level l of C which is not in F, at most v of its subsets fro...

Ngày tải lên: 07/08/2014, 21:20

... (called groups), and A is a collection of subsets (called blocks) of X with |A| ∈ K for any A ∈ A, such that every pair of points from distinct groups occurs in exactly λ blocks and no pair of points ... in each row contain every element of X \ G 3 times and no element of G for some G ∈ G. The obvious necessary conditions for the existence of an FGDRP(3, g u ) are u...

Ngày tải lên: 07/08/2014, 21:21

... corollaries, and thus, our main result provides purely combinatorial proofs for the Erd˝os-Heilbronn conjecture and an inverse Erd˝os-Heilbronn theorem. 1 Introduction For A a subset of an abelian group, ... critical pairs of subsets of a group of prime order, J. London Math. Soc. 31 (1 956 ), 200–2 05. the electronic journal of combinatorics 16 (2009), #R100 8 Our main r...

Ngày tải lên: 08/08/2014, 01:20

... sets of G x,z 1 and G x,z 2 coincide. Hence, also the graphs G x,z 1 and G x,z 2 coincide. The lemma now follows from the above discussion and the connectedness of C.  For every point x of S and ... crucial for the remainder of the proof. Lemma 2.8 The point-line geometry D x is a symmetric 2-( 25, 9, 3)-design for every point x of S. As a consequence, if B 1 and B...

Ngày tải lên: 08/08/2014, 12:23