On local edge intersection graphs of paths on bounded degree trees
نویسندگان
چکیده
An undirected graph G is called an EPT graph if it is the edge intersection graph of a family of paths in a tree. We call G a local EPT graph if it is the EPT graph of a collection of paths P which all share a common vertex. In this paper, we characterize the local EPT graphs which can be represented in a host tree with maximum degree h.
منابع مشابه
A New Heuristic Algorithm for Drawing Binary Trees within Arbitrary Polygons Based on Center of Gravity
Graphs have enormous usage in software engineering, network and electrical engineering. In fact graphs drawing is a geometrically representation of information. Among graphs, trees are concentrated because of their ability in hierarchical extension as well as processing VLSI circuit. Many algorithms have been proposed for drawing binary trees within polygons. However these algorithms generate b...
متن کاملEdge and vertex intersection of paths in a tree
In this paper we continue the investigation of the class of edge intersection graphs of a collection of paths in a tree (EPT graphs) where two paths edge intersect if they share an edge. The class of EPT graphs differs from the class known as path graphs, the latter being the class of vertex intersection graphs of paths in a tree. A characterization is presented here showing when a path graph i...
متن کاملEdge intersection graphs of systems of grid paths with bounded number of bends
We answer some of the questions raised by Golumbic, Lipshteyn and Stern regarding edge intersection graphs of paths on a grid (EPG graphs). We prove that for any d ≥ 4, in order to represent all n vertex graphs with maximum degree d as edge intersection graphs of n paths, a grid of area Θ(n2) is needed. A bend is a turn of a path at a grid point. Let Bk be the class of graphs that have an EPG r...
متن کاملEdge Disjoint Paths and Multicut Problems in Graphs Generalizing the Trees∗
We generalize all the results obtained for maximum integer multiflow and minimum multicut problems in trees by Garg et al. [Primaldual approximation algorithms for integral flow and multicut in trees. Algorithmica 18 (1997) 3–20] to graphs with a fixed cyclomatic number, while this cannot be achieved for other classical generalizations of the trees. Moreover, we prove that the minimum multicut ...
متن کاملOn the Size-Ramsey Number of Hypergraphs
The size-Ramsey number of a graph G is the minimum number of edges in a graph H such that every 2-edge-coloring of H yields a monochromatic copy of G. Size-Ramsey numbers of graphs have been studied for almost 40 years with particular focus on the case of trees and bounded degree graphs. We initiate the study of size-Ramsey numbers for k-uniform hypergraphs. Analogous to the graph case, we cons...
متن کامل