A chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path  $P$ is called a monophonic path if it is a chordless path. A longest $x-y$ monophonic path is called an $x-y$ detour monophonic path. A  detour monophonic graphoidal cover of a graph $G$ is a collection $psi_{dm}$ of detour monophonic paths in $G$ such that every vertex of $G$ is an internal vertex  of at most on...

In this paper, we study cooperative games arising from fractional edge covering problems on graphs. We introduce two games, a rigid fractional edge covering game and its relaxed game, as generalizations of a rigid edge covering game and its relaxed game studied by Liu and Fang [4]. We show that main results in [4] are well extended to fractional edge covering games. That is, we give a character...

A set P of edge-disjoint paths in a graph G is called an edge-covering of G if every edge of G is contained in a path of P. The path edge-covering number of G is then defined as the smallest number p(G) of paths in such an edge-covering of G. This parameter appeared in the study of certain models of information retrieval structures (see, e. g., [6]). If we are considering a tree T , then it is ...

In the Maximum cost m′-subgraph problem we are given an undirected simple graph G(V,E) with weights w(v) on the vertices. The goal is to select a set U ⊆ V so that the number of edges with at least one endpoint in U is at most m′ with maximum weight W ∗. In [11] a ratio 3 approximation is given for problem. We improve this result by giving a 2 + approximation for the problem, for every constant...

Keywords: Uncertainty modelling Edge cover Random fuzzy programming Random fuzzy simulation Genetic algorithm a b s t r a c t Edge covering problem (ECP) is to find an edge cover with the minimum weight in a graph. By quantifying costs, time or opponent's payoffs as weights on edges, ECP is employed to model many real-life problems in engineering and management. Since various types of uncertain...

The edge clique cover sum number (resp. edge clique partition sum number) of a graph G, denoted by scc(G) (resp. scp(G)), is defined as the smallest integer k for which there exists a collection of complete subgraphs of G, covering (resp. partitioning) all edges of G such that the sum of sizes of the cliques is at most k. By definition, scc(G) 5 scp(G). Also, it is known that for every graph G ...