for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.

In this paper, we introduce certain concepts, including neutrosophic hypergraph, line graph of neutrosophic hypergraph, dual neutrosophic hypergraph, tempered neutrosophic hypergraph and transversal neutrosophic hypergraph. We illustrate these concepts by several examples and investigate some of interesting properties. Key-words: Neutrosophic hypergraph, Line graph of neutrosophic hypergraph, D...

Graph theory has been a useful tool for logic programming in many aspects. In this paper, we propose an equivalent representation of multi-adjoint programs using hypergraphs, which are generalization classical graphs that allows the use hypergraph programming. Specifically, considered paper to increase level and flexibility different termination results computation least model fuzzy via immedia...

Abstract This chapter introduces three hypergraph computation paradigms, including intra-hypergraph computation, inter-hypergraph and structure computation. Intra-hypergraph representation aims to conduct learning of a hypergraph, where each subject is represented by its components. Inter-hypergraph vertices in the vertex hypergraph. Hypergraph prediction, which find connections among vertices....

Abstract Hypergraph modeling is the fundamental task in hypergraph computation, which targets on establishing a high-quality structure to accurately formulate high-order correlation among data. In this section, we introduce different methods show how build hypergraphs using various pieces of information, such as features, attributes, and/or graphs. These are organized into two broad categories,...

The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph pLaplacian. Unlike the existing two-node graph Laplacians, this generalization makes it possible to ana...

With the advent of big data and information age, magnitude various complex networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary networks, while hypergraphs have ability to describe characterize higher order relationships, which attracted extensive attention from academia industry in recent years. Firstly, this paper described development process, application ar...

Neutrosopic sets were introduced by Smarandache [2] which are the generalization of fuzzy sets and intuitionistic fuzzy sets. The Neutrosophic sets have many applications in medical, management sciences, life sciences and engineering, graph theory, robotics, automata theory and computer science. The single valued neutrosophic graphs were introduced by Broumi, Talea, Bakali and Smarandache [5]. ...