A graph G is called (K3,K3)-co-critical if the edges of G can be coloured with two colours without getting a monochromatic triangle, but adding any new edge to the graph, this kind of ’good’ colouring is impossible. In this short note we construct (K3,K3)-co-critical graphs of maximal degree O(n3/4).

Nikulin has classified all finite abelian groups acting symplectically on a K3 surface and he has shown that the induced action on the K3 lattice U⊕E8(−1) depends only on the group but not on the K3 surface. For all the groups in the list of Nikulin we compute the invariant sublattice and its orthogonal complement by using some special elliptic K3 surfaces.

In this paper, we consider the metric packing problem for the commodity graph of disjoint two triangles K3 +K3, which is dual to the multiflow feasibility problem for the commodity graph K3 + K3. We prove Karzanov’s conjecture concerning quarter-integral packings by certain bipartite metrics.

We apply the method of algebraic deformation to N-tuple of algebraic K3 surfaces. When N=3, we show that the deformed triplet of algebraic K3 surfaces exhibits a deformed hyperkähler structure. The deformation moduli space of this family of noncommutatively deformed K3 surfaces turns out to be of dimension 57, which is three times of that of complex deformations of algebraic K3 surfaces.

Minuman sari lemon kolagen merupakan salah satu minuman fungsional yang mudah diserap oleh tubuh, namun berasal dari ikan memiliki aroma amis sehingga dapat dikombinasikan dengan buah untuk menutupi tersebut. Penelitian ini bertujuan memperoleh konsentrasi tepat menghasilkan berbasis karakteristik fisikokimia, mikrobiologi, dan sensori terbaik. menggunakan Rancangan Acak Kelompok Lengkap (RAKL)...

introduction: the most important aims of root canal preparation are the removal of vital pulp tissue, remaining necrotic debris and infected dentin, eliminating the bulk of bacteria present in the root canal system. the aim of this study was to compare the cleaning efficacy of hand k-flexofiles and rotary race and k3 instruments in root canal preparation. materials and methods: a total of 60 si...

In this paper, we consider the metric packing problem for the commodity graph of disjoint two triangles K3+K3, which is dual to the multiflow feasibility problem for the commodity graph K3 +K3. We prove a strengthening of Karzanov’s conjecture concerning quarter-integral packings by certain bipartite metrics.

Examples 1. A K3 surface of degree two is a double cover of P, ramified in a smooth sextic. K3 surfaces of degree four are smooth quartics in P. A K3 surface of degree six is a smooth complete intersection of a quadric and a cubic in P. And, finally, K3 surfaces of degree eight are smooth complete intersections of three quadrics in P. The Picard group of a K3 surface is isomorphic to Zn where n...