RAINBOW CONNECTION NUMBERS OF SOME S-OVERLAPPING R-UNIFORM HYPERGRAPH WITH SIZE T CLASSES

• Main Author: Alief Farihati, Sitta
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/87762
• Institution: Institut Teknologi Bandung

In 2014, Carpentier et al. introduced the rainbow connection number concept of hypergraphs. The concept extends the rainbow connection number concept on graphs developed by Chartrand et al. The concept of rainbow connection numbers on hypergraphs has been implemented on minimally connected hypergraphs and several classes of r-uniform hypergraphs, namely complete hypergraphs, cycle hypergraphs, and multipartite hypergraphs so that the rainbow connection numbers of these hypergraph classes have been obtained. In this dissertation, we study the rainbow connection numbers of some classes of r-uniform connected hypergraphs, focusing on some classes of s-overlapping r-uniform hypergraphs with size t. For r 2, 1 s < r, and t 1, an s-overlapping r-uniform hypergraphs with size t, denoted by Hr s;t, is an r-uniform connected hypergraph whose every pair of adjacent edges intersects at most s vertices and there exists a pair of adjacent edges intersects exactly s vertices. The collection of s-overlapping r-uniform hypergraphs with size t is denoted by Hr s;t. This study determines the lower bound of the rainbow connection number of any hypergraph. In addition, the rainbow connection number of some classes of s- overlapping r-uniform hypergraphs with size t, which are either hypertrees or hypercycles, are also determined. A hypertree is a hypergraph whose host is a tree graph. A hypercyclic is a hypergraph that contains one or more cycle hypergraphs. The cycle hypergraph is a hypergraph whose host is a cycle graph. The host graph of a hypergraph is a connected graph over the same vertex set as the hypergraph, and each edge in the hypergraph induces a connected subgraph of the graph.