Báo cáo toán học: "Two Extremal Problems in Graph Theory" pot

... H are graphs, then their union is the graph G ∪ H consisting of disjoint copies of G and H.Ifm is a positive integer, then mG is the graph consisting of m disjoint copies of G. We call a graph ... A in I whichisjoinedtofewerthanq/2 trees of odd order. As in the preceding paragraph we obtain an independent set of G of size greater than (n − 1)/2, contradicting the assumption that G i...

Ngày tải lên: 07/08/2014, 06:20

... decreasing (resp. increasing), and so the log-concavity implies the unimodality. The unimodality problems, including concavity (convexity) and log- concavity (log-convexity), arise naturally in many ... precisely in one of d − 2 open intervals  k d , k+1 d  , where k = 1, . . . , d − 2. Indeed, neither two terms of  j δ  δ−1 j=1 nor two terms of  j d−δ  d−δ−1 j=1 are in the same...

Ngày tải lên: 07/08/2014, 21:20

... subgraphs of hypercubes, J. Graph Theory 17 (1993), 477– 479. [10] P. Erd˝os, O n extremal problems of graphs and generalized graphs, Israel J. Math. 2 (1964), 183–190. [11] P. Erd˝os, On some problems ... edge formed by replacing b g(i ℓ ) in f(u) with a flip-bit is in G. But this edge is just the edge between f(u) and f(v). We therefore have an embedding of H in G, completing t...

Ngày tải lên: 08/08/2014, 12:22

... eects monitoring plays an important role in marine monitoring. Contaminants and their eects on sh as well as on other marine organisms belong to the main topics of international monitoring schemes. ... drawbacks of choosing and applying marker of contaminant eects to marine eld samples. It reects the actual stage of international guidelines for biological eects monitoring in mari...

Ngày tải lên: 20/06/2014, 20:20

... least 2m −2 −j whichcombinedwiththe inequality in (5.35) yields that degree(R j )=2m − 2 − j (5.38) completing the induction. Now setting t = u/v in (5.35) and mutiplying both sides by v 2m−2−j ,gives v 2j v 2m−2−j R j (u/v)=v j−1 a i (u/v)v 2m−1 P ... possess a rich combinatorial underpinning resulting in truly surprising identities. The S n case deserves special attention since the re...

Ngày tải lên: 07/08/2014, 08:22

... new graph G ∗ by using two copies of G − u and joining two sets of vertices {x 1 ,x 2 , ,x 2r } by a matching M. Then the resulting graph G ∗ is a 2m-regular graph with 2(|V (G)|−1) vertices. Since ... 1-factor containing e,so does G ∗ . By Theorem 1, G ∗ has a k-factor containing e and another k-factor avoiding e for all k,1≤ k ≤ 2r − 1. Deleting the matching M from G ∗ ,weobtaina[k, k...

Ngày tải lên: 07/08/2014, 08:22

... is not completely contained inside R ∗ , the center of S is inside R ∗ , S does not contain any point in Q as its interior point, and there is no line segment L i ∈ U that intersects two nonadjacent ... is not completely contained inside R ∗ , the center of S is inside R ∗ , S does not contain any point in Q as its interior point, and there is no line segment L i ∈ U that intersects two n...

Ngày tải lên: 07/08/2014, 13:21

... able to show that in the domains θ = o  √ λ min /a(r) 2  and 1/θ = O  √ λ min  the inequality (V) is certainly true 1 . But since √ λ min /a(r) 2 = o  1/ √ λ min  there is a gap ... B(r) ε , we obtain det B(r) = O  r σd(dL+1) min  . On setting η = r − e 3 min this implies max θ∈∆(r) |ε(r, θ)| = O  r σd(Ld+1)ε min · r − e 2 min r − e 3 min  → 0 for r min → ∞ because of ......

Ngày tải lên: 07/08/2014, 13:21

... property that any minor of a graph G in the family (a simple graph formed from G by contracting edges and removing edges and vertices) remains in the family. The friendship graphs (graphs in the form ... triangles sharing a common vertex) are not minor-closed, but are the maximal graphs in another minor-closed family, the graphs formed by adding a single vertex to a matching. For...

Ngày tải lên: 08/08/2014, 12:22

... regression model including three-linear lines in 6π interval is explained in detail . The proposed LS criterion using the multiple lin- ear regression model is given as ˆτ E,d = arg min τ 1  m=−1  l |(ω l τ ... wrapping results in disconti- nuity due to the shifting phase term, ±2π given in Equa- tion 3. The purpose of phase expansion proposed in this article is recovering linear...

Ngày tải lên: 20/06/2014, 20:20