Báo cáo toán học: "The Tur´n problem for hypergraphs of fixed size " ppsx

... The Tur´an problem for hypergraphs of fixed size Peter Keevash Department of Mathematics Caltech, Pasadena, CA 91125, USA. keevash@caltech.edu Submitted: ... a forest of given size. Lemma 2 (i) An r-uniform hypergraph with at least r!(t − 1) r edges contains a forest with t edges. (ii) Let F be a 3-uniform hypergraph. Then either (a) F contains a forest ... bounds are known...

Ngày tải lên: 07/08/2014, 08:22

... )  n k  exists. See [4] for a survey on the Tur´an problem for hypergraphs. The value of π(F ), for k ≥ 3, is known for very few F and any addition to this list is of interest. In this note ... the Tur´an number of triple systems, J. Combin. Theory (A) 100 (2002), 135–152. the electronic journal of combinatorics 10 (2003), #R18 7 3 Proof of Theorem 1 The proof consists...

Ngày tải lên: 07/08/2014, 07:21

... h 3" alt =""

Ngày tải lên: 05/08/2014, 15:21

... these results, we include a proof of Theorem 1.1 for completeness. 2.1 A characterization for faces For convenience, let [n] := {1, 2 . . . , n} be the set of vertices of CP(n, d), numbered ac- cording ... then  n k  q=ω =  a c  b d  q=ω . Proof of Theorem 1.3. For r  2 a divisor of n, let ω be a primitive rth root of unity and let C r be the subgroup of order r...

Ngày tải lên: 08/08/2014, 12:22

... structure of G. Along the spirit of Tur´an Theory we consider the problem of finding the maximum of e p (G) over the class of graphs which contain no copy of prescribed forbidden ∗ e-mail: yairc@macam98.ac.il † e-mail: ... examination of the proof of Theorem 1.2 shows that the value of n 0 (k) in the statement of the theorem is O(k 2 ). Another thing to note is that, as l...

Ngày tải lên: 07/08/2014, 06:20

... the vertex sets of π are of size one or two. Finally, for k ≥ 3 a tip may be of arbitrary size thus a vertex set of π can be of arbitrary size as well. Because the ground set of the matroid M ... graphs G the size of the maximum F-packings of G can be determined in time polynomial in the size of G. (The size of a graph is the number of its vertices.) Severa...

Ngày tải lên: 07/08/2014, 08:22

... x 0 (t) of the perturbed system (3.1) is a solution of some linear system of form (3.3),whereF (t)x is of the same order of smallness as f (t, x), i.e. F (t)  δ(t), ∀t ∈ R + . (3.4) Proof. From ... R(t)isaC-function of im P(t) of (3.11). Thus, C-classes R of (2.1) and R U imP of the invariant subspace im P of the solution space of (3.11) coincide. Suppose that x δ (t)...

Ngày tải lên: 06/08/2014, 05:20

... face of G is of size ≤ 6. Proof. Observe that G−V (C) is an outerplanar graph. So it is 3-choosable. The fact that every face of G is of size ≤ 6 can be easily proved by induction on the number of ... 4-coloring of G, and hence c uses both colors on K. Therefore, c is a 2-coloring of H(G). For the skeptics of the proof of the 4-Color Theorem and since we do not want to...

Ngày tải lên: 07/08/2014, 06:20

... boundary of the edge set of a cycle is empty. The boundary of the set of 4-cycles of a cube is also empty, as is the boundary of any set of vertices. For j ≥ 1, define a j- N circuit to be any set S of ... boundary of an edge consists of its two endpoints, the boundary of a K 2,2 consists of the four edges of that 4-cycle, the boundary of a K 2,3 consists of its...

Ngày tải lên: 07/08/2014, 07:21

... vertices of p a are completely joined to the vertices of p b in G. Proof. Assume (to reach a contradiction) that the lemma is false. Of all counterexamples, pick an optimal coloring C of G, {a}, ... all we need to check is that the union of any m − 2 of lists has at least m − 2 elements and that the union of all of the lists has m − 1 elements. If the former were false, then s...

Ngày tải lên: 07/08/2014, 15:22