Agent systems have become more and more important in computer science. They allow to implement complex distributed systems composed of communicating autonomous entities. Transformation units constitute a structuring principle for graph transformation systems which split up large sets of rules, but still graphs are transformed as a whole. Recently, distributed transformation units have been intr...

We introduce I/O-effiient certifying algorithms for bipartite graphs, as well the classes of split, threshold, chain, and trivially perfect graphs. When input graph is a member respective class, algorithm returns certificate that characterizes this class. Otherwise, it forbidden induced subgraph non-membership. On with n vertices m edges, our take $$O( {\textsc {sort}(n + m)} ) $$ I/Os in worst...

Let K(G) be the clique graph of a graph G. A m-weighting of K(G) consists on giving to each m-size subset of its vertices a weight equal to the size of the intersection of the m corresponding cliques of G. The 2weighted clique graph was previously considered by McKee. In this work we obtain a characterization of weighted clique graphs similar to Roberts and Spencer’s characterization for clique...

Parity graphs form a superclass of bipartite and distance-hereditary graphs. Since their introduction, all the algorithms proposed as solutions to the recognition problem and other combinatorial problems exploit the structural property of these graphs described by Burlet and Uhry in [8]. This paper introduces a different structural property of parity graphs: split decomposition returns exactly,...

This paper discusses the Flow-Orientation Problem (FOP), which assigns orientations of all links of an undirected network to obtain a directed network for meeting some flow optimization measurements. First, we describe the background and define three related FOP issues: MDFOP, MDSFOP, and MDDFOP. We discuss the complexity of the FOP on general networks, and also list the essences of convex-spli...

Listing, generating or enumerating objects of specified type is one of the principal tasks in algorithmics. In graph algorithms one often enumerates vertex subsets satisfying a certain property. We study the enumeration of all minimal connected dominating sets of an input graph from various graph classes of bounded chordality. We establish enumeration algorithms as well as lower and upper bound...

Lexicographic Breadth First Search (LBFS) is one of fundamental graph search algorithms that has numerous applications, including recognition of graph classes, computation of graph parameters, and detection of certain graph structures. The well-known result on the end-vertices of LBFS of chordal graphs has tempted researchers to study the end-vertices of LBFS of various classes of graphs, inclu...

For fixed integers r, l ≥ 0, a graph G is called an (r, l)-graph if the vertex set V (G) can be partitioned into r independent sets and l cliques. This brings us to the following natural parameterized questions: Vertex (r, l)-Partization and Edge (r, l)-Partization. An input to these problems consist of a graph G and a positive integer k and the objective is to decide whether there exists a set...

A t-spanner of a graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times their distance in G. Spanners arise in the context of approximating the original graph with a sparse subgraph (Peleg, D., and Scha ffer, A. A. (1989), J. Graph. Theory 13 (1), 99 116). The MINIMUM t-SPANNER problem seeks to find a t-spanner with the minimum number of edges f...

A path in an edge-colored graph G is rainbow if no two edges of it are colored the same. The graph G is rainbow-connected if there is a rainbow path between every pair of vertices. If there is a rainbow shortest path between every pair of vertices, the graph G is strongly rainbow-connected. The minimum number of colors needed to make G rainbow-connected is known as the rainbow connection number...