Báo cáo toán học: "Saturation Numbers of Books" ppsx

... set X of b − 1 vertices, each of degree n − 1, a clique L of p 2 vertices, a the electronic journal of combinatorics 15 (2008), #R118 7 Saturation Numbers of Books Guantao Chen ∗ Dept. of Math. ... has a set X of b−1 vertices, each of degree n − 1, a clique L of p 2 vertices, a set T of n − p/2 − b + 1 vertices inducing an almost (p − 1)-regular graph which contains a ve...

Ngày tải lên: 07/08/2014, 21:20

... the number of bristles. So, B r,k contains r + k vertices. (See Figure 4.) The vertex of degree k + 1 will be referred to as the center of the broom. One of the interesting properties of the collection ... Let G ∈ SAT(n, T k ) for a fixed tree T k of order k ≥ 5. Observe that any component of G of order less than k must be complete and the union of any pair of components mu...

Ngày tải lên: 08/08/2014, 01:20

... 1)y k +1. This completes the proof of (7) and verification of the upper bound. The proof of Theorem 1 is complete. Note that, by (7) and the remark following the proof of (6), all the orientations ... pleasing characterization of these integer vectors. We do have a couple of observations about this the electronic journal of combinatorics 12 (2005), #R17 29 Splitting Numbers of...

Ngày tải lên: 07/08/2014, 08:22

... examples of fixing sets of non-trivial finite groups are of the form {1, . . . , k } for some k. If the fixing set of every non-trivial finite group is of this form, then the computation of a fixing ... fix(Inf k (K n )) = ⌈ n−1 k+1 ⌉. Proof. The statement is clear for k = 0, so assume k > 0. Since each vertex of Inf k (K n ) is labeled with a sequence of the numbers {1, . . ....

Ngày tải lên: 07/08/2014, 21:21

... Gale- maximality of v to argue that if v lies in some face P of C ≤α , then P ⊆ P v,α . We give this argument explicitly below for only one of the five kinds of ideals, namely those of the form I(F ... {b 3 } × {c 4 }. Proof of Claim (b): If v is not the only vertex of C ≤α , then because v is Gale-maximal, without loss of generality we may assume that there is another vertex v...

Ngày tải lên: 08/08/2014, 01:20

... bounds on the isoperimetric numbers and bisection widths of a large class of regular graphs of high degree. Our methods are com- binatorial and do not require a knowledge of the eigenvalue spectrum. ... pieces A a nd B. The isoperimetric number of a graph is a discrete version of the Cheeger constant of a manifold. Upper bounds on the isoperimetric numbers of the Cayley gr...

Ngày tải lên: 08/08/2014, 14:23

... symbol of σ.Sincen +1>m, we can select a random subsequence of σ of length m by first throwing out one of the n + 1 symbols of σ at random and then randomly selecting a subsequence of length ... the following theorem of Stromquist. We give a proof which is somewhat shorter than the proof in [1], both for its own interest and because we will reuse the method of proof when stu...

Ngày tải lên: 07/08/2014, 08:22

... proof of Theorem 1. Lemma 7. Let P be a hereditary property of tournaments. If B(P) = ∞, then P contains arbitrarily large structures of Type 1 or 2. Proof. Let P be a hereditary property of ... proof of Theorem 28 of [4] can also be adapted to hereditary properties of tour- naments, to produce many properties with different exponential speeds, but we spare the reader the details...

Ngày tải lên: 07/08/2014, 15:23

... of rows of W is linearly dependent, then the corresponding collection of rows of S 1 is also linearly dependent). In particular, no pair of rows of W is linearly dependent. Let α be a cycle of ... LNS(W), the set of rows of W indexed by α is linearly independent. We have shown: whenever a collection of rows of S 1 is linearly independent, the corresponding collection of...

Ngày tải lên: 07/08/2014, 15:23

... is, there are copies of C 4 if n ≡ 0 (mod 4) and there are copies of C 4 and one copy of C 6 if n ≡ 2 (mod 4). 3.3 Alternate proof of CR(C n ) In the same vein as the above proof fo r CR(R n,2 ) ... direction of Conjecture 3 .3 is the fo llowing proposition. the electronic journal of combinatorics 16 (2009), #R54 13 The Maximum of the Maximum Rectilinear Crossing Numbers of...

Ngày tải lên: 07/08/2014, 21:21