Paul Seymour conjectured that any graph G of order n and minimum degree at least k k+1n contains the k th power of a Hamilton cycle. We prove the following approximate version. For any > 0 and positive integer k, there is an n0 such that, if G has order n ≥ n0 and minimum degree at least ( k k+1 + )n, then G contains the kth power of a Hamilton cycle. c © 1998 John Wiley & Sons, Inc. J Graph Th...

We exploit the Galois symmetries of little disks operads to show that many differentials in Goodwillie–Weiss spectral sequences approximating homology and homotopy knot spaces vanish at a prime $p$ . Combined with recent results on relationship between embedding calculus finite-type theory, we deduce $(n+1)$ th approximation is -local universal Vassiliev invariant degree $\leq n$ for every $n \...

Let E be an elliptic curve defined over ℚ, and let ρ :Gal(ℚ ¯/ℚ)→GL(2,ℤ ^) the adelic representation associated to natural action of Galois on torsion points E(ℚ ¯). By a theorem Serre, image is open, but always index at least 2 in GL(2,ℤ due certain quadratic entanglement amongst division fields. In this paper, we study other types abelian entanglements. More concretely, classify curves E/ℚ, p...

let $g = (v, e)$ be a simple graph. denote by $d(g)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $a(g)$ the adjacency matrix of $g$. the  signless laplacianmatrix of $g$ is $q(g) = d(g) + a(g)$ and the $k-$th signless laplacian spectral moment of  graph $g$ is defined as $t_k(g)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

Suppose that the conditional distributions of x˜ (resp. y˜) can be ranked according to m-th n-th) risk order. Increasing their statistical concordance increases (m,n) degree riskiness (x˜,y˜), i.e., it reduces expected utility for all bivariate functions whose sign cross-derivative is (?1)m+n+1. This means in particular this increase risks induces a m+n x˜+y˜. On basis these general results, I ...