A (hyper)graph G is called k-critical if it has chromatic number k, but every proper sub(hyper)graph of it is (k− 1)-colourable. We prove that for sufficiently large k, every k-critical triangle-free graph on n vertices has at least (k−o(k))n edges. Furthermore, we show that every (k+1)-critical hypergraph on n vertices and without graph edges has at least (k−3/ 3 √ k)n edges. Both bounds diffe...

Hypercubes and star graphs are widespread topologies of interconnection networks. The class of hyper-stars was introduced as a new type of interconnection network to compete with both hypercubes and star graphs, and the class of folded hyper-stars is a strengthened variation of hyperstars with additional links to connect nodes with complemented 0/1-strings. Constructing independent spanning tre...

We pursue the study of the computational power of Piecewise Constant Derivative PCD systems started in PCD systems are dynamical systems de ned by a piecewise constant di erential equation and can be considered as computational machines working on a continuous space with a continuous time We prove that the languages recognized by rational PCD systems in dimension d k respectively d k k in nite ...

A light Higgs portal scalar could be abundantly produced in the earth's atmosphere and decay large-volume neutrino detectors. We point out that Hyper-Kamiokande detector bears a strong discovery potential of probing such particles an uncharted parameter space is actively explored by intensity frontier experiments including rare kaon decays. The signal we propose to look for electron-positron pa...

in this paper rst we de ne the notions of positive implicativehyper mv -ideals of types 1,2,3 and 4 in hyper mv -algebras and we investigatethe relationship between of them . then by some examples we show that thesenotions are not equivalent. finally we give some relations between these notionsand the notions of (weak) hyper mv -ideals and (weak) hyper mv -deductivesystems of hyper mv -algebras.

Interval variables can be measured on very different scales. We first remind a general methodology used for measuring the dispersion of a variable from an optimal center and we define two measures of dispersions associated to two optimal ”centers” for interval variables. Then we study the relations between the standardization of a data table and the use in clustering of a normalized distance. F...

We consider the Hypergraph Multiway Partition problem (Hyper-MP). The input consists of an edge-weighted hypergraph G = (V, E) and k vertices s1, . . . , sk called terminals. A multiway partition of the hypergraph is a partition (or labeling) of the vertices of G into k sets A1, . . . , Ak such that si ∈ Ai for each i ∈ [k]. The cost of a multiway partition (A1, . . . , Ak) is ∑k i=1 w(δ(Ai)), ...