Low-distortion embeddings of trees.
Lower and upper bounds of shortest paths in reachability graphs.
Memory paging for connectivity and path problems in graphs.
Mineurs d'arbres avec racines
Minimal 2-dominating sets in trees
We provide an algorithm for listing all minimal 2-dominating sets of a tree of order n in time 𝒪(1.3248n). This implies that every tree has at most 1.3248n minimal 2-dominating sets. We also show that this bound is tight.
Minimum convex-cost tension problems on series-parallel graphs
We present briefly some results we obtained with known methods to solve minimum cost tension problems, comparing their performance on non-specific graphs and on series-parallel graphs. These graphs are shown to be of interest to approximate many tension problems, like synchronization in hypermedia documents. We propose a new aggregation method to solve the minimum convex piecewise linear cost tension problem on series-parallel graphs in operations.
Minimum convex-cost tension problems on series-parallel graphs
We present briefly some results we obtained with known methods to solve minimum cost tension problems, comparing their performance on non-specific graphs and on series-parallel graphs. These graphs are shown to be of interest to approximate many tension problems, like synchronization in hypermedia documents. We propose a new aggregation method to solve the minimum convex piecewise linear cost tension problem on series-parallel graphs in O(m3) operations.
Minimum eccentricity multicast trees.
Minimum survivable graphs with bounded distance increase.
Minimum vertex ranking spanning tree problem for chordal and proper interval graphs
A vertex k-ranking of a simple graph is a coloring of its vertices with k colors in such a way that each path connecting two vertices of the same color contains a vertex with a bigger color. Consider the minimum vertex ranking spanning tree (MVRST) problem where the goal is to find a spanning tree of a given graph G which has a vertex ranking using the minimal number of colors over vertex rankings of all spanning trees of G. K. Miyata et al. proved in [NP-hardness proof and an approximation algorithm...
More on the complexity of cover graphs
In response to [3] and [4] we prove that the recognition of cover graphs of finite posets is an NP-hard problem.
Morphing planar graphs in spherical space.
Motion planning in cartesian product graphs
Let G be an undirected graph with n vertices. Assume that a robot is placed on a vertex and n − 2 obstacles are placed on the other vertices. A vertex on which neither a robot nor an obstacle is placed is said to have a hole. Consider a single player game in which a robot or obstacle can be moved to adjacent vertex if it has a hole. The objective is to take the robot to a fixed destination vertex using minimum number of moves. In general, it is not necessary that the robot will take a shortest path...
Multicolored isomorphic spanning trees in complete graphs.
Multidimensional linear congruential graphs
Multiprocessor Interconnection Networks
Multi-static enumeration of two-stack sortable permutations.
Navigating clustered graphs using force-directed methods.
Neochromatica
We create and discuss several modifications to traditional graph coloring. In particular, we classify various notions of coloring in a proper hierarchy. We concentrate on grid graphs whose colorings can be represented by natural number entries in arrays with various restrictions.
New bounds for codes identifying vertices in graphs.