We study the approximation complexity of the Minimum Edge Dominating Set problem in everywhere ǫ-dense and average ǭ-dense graphs. More precisely, we consider the computational complexity of approximating a generalization of the Minimum Edge Dominating Set problem, the so called Minimum Subset Edge Dominating Set problem. As a direct result, we obtain for the special case of the Minimum Edge Do...

Consider edge-colorings of the complete graph Kn. Let r(n, t) be the maximum number of colors in such a coloring that does not have t edge-disjoint rainbow spanning trees. Let s(n, t) be the maximum number of colors in such a coloring having no rainbow spanning subgraph with diameter at most t. We prove r(n, t) = (n−2 2 )

This study aims at exploring postcolonial themes raised by Andrea Hirata’s Laskar Pelangi (Rainbow Warriors). Specifically, it will reveal the characteristics of hybridity found in the novel that prove this literary work may be categorized as postcolonial writing despite the fact that western or white colonialism has no impact or trace at all in the novel. Furthermore, the study will prove that...

An edge-coloured path is rainbow if the colours of its edges are distinct. For a positive integer k, an edge-colouring of a graph G is rainbow k-connected if any two vertices of G are connected by k internally vertex-disjoint rainbow paths. The rainbow k-connection number rck(G) is defined to be the minimum integer t such that there exists an edge-colouring of G with t colours which is rainbow ...

An r-edge-coloring of a graph is an assignment of r colors to the edges of the graph. An exactly r-edge-coloring of a graph is an r-edge-coloring of the graph that uses all r colors. A matching of an edge-colored graph is called rainbow matching, if no two edges have the same color in the matching. In this paper, we prove that an exactly r-edge-colored complete graph of order n has a rainbow ma...

A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such ...

Let H be an edge colored hypergraph. We say that H contains a rainbow copy of a hypergraph S if it contains an isomorphic copy of S with all edges of distinct colors. We consider the following setting. A randomly edge colored random hypergraph H ∼H k c (n, p) is obtained by adding each k-subset of [n] with probability p, and assigning it a color from [c] uniformly, independently at random. As a...

a roman dominating function (rdf) on a graph g = (v,e) is defined to be a function satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. a set s v is a restrained dominating set if every vertex not in s is adjacent to a vertex in s and to a vertex in . we define a restrained roman dominating function on a graph g = (v,e) to be ...

A path in an edge colored graph is said to be a rainbow path if every edge in this colored with the same color. A vertex-colored graph G is rainbow vertex-connected if any pair of vertices in G are connected by a path whose internal vertices have distinct colors. The rainbow vertexconnection number of G denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainb...

Brualdi and Hollingsworth conjectured that, for even n, in a proper edge coloring of Kn using precisely n − 1 colors, the edge set can be partitioned into n2 spanning trees which are rainbow (and hence, precisely one edge from each color class is in each spanning tree). They proved that there always are two edge disjoint rainbow spanning trees. Kaneko, Kano and Suzuki improved this to three edg...