The edge intersection graphs of paths in a tree
نویسندگان
چکیده
The class of edge intersection graphs of a collection of paths in a tree (EPT graphs) is investigated, where two paths edge intersect if they share an edge. The cliques of an EPT graph are characterized and shown to have strong Helly number 4. From this it is demonstrated that the problem of finding a maximum clique of an EPT graph can be solved in polynomial time. It is shown that the strong perfect graph conjecture holds for EPT graphs. Further complexity results follow from the observation that every line graph is an EPT graph. The class of EPT graphs is equivalent to the class of fundamental cycle graphs.
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 کاملThe recognition of k-EPT graphs
We consider a generalization of edge intersection graphs of paths in a tree. Let P be a collection of nontrivial simple paths in a tree T . We define the k-edge (k ≥ 1) intersection graph Γk(P), whose vertices correspond to the members of P, and two vertices are joined by an edge if the corresponding members of P share k edges in T . An undirected graph G is called a k-edge intersection graph o...
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 کاملThe k-edge intersection graphs of paths in a tree
We consider a generalization of edge intersection graphs of paths in a tree. Let P be a collection of nontrivial simple paths in a tree T . We define the k-edge (k 1) intersection graph k(P), whose vertices correspond to the members of P, and two vertices are joined by an edge if the corresponding members ofP share k edges in T . An undirected graphG is called a k-edge intersection graph of pat...
متن کاملRepresentations of Edge Intersection Graphs of Paths in a Tree
Let P be a collection of nontrivial simple paths in a tree T . The edge intersection graph of P , denoted by EPT (P), has vertex set that corresponds to the members of P , and two vertices are joined by an edge if the corresponding members of P share a common edge in T . An undirected graph G is called an edge intersection graph of paths in a tree, if G = EPT (P) for some P and T . The EPT grap...
متن کاملGraphs of edge-intersecting and non-splitting paths
The families of Edge Intersection Graphs of Paths in a tree (resp. in a grid) EPT (resp. EPG) are well studied graph classes. Recently we introduced the class of graphs of Edge-Intersecting and NonSplitting Paths in a Tree (ENPT) [2]. In this model, two vertices are adjacent if they represent two intersecting paths of a tree whose union is also a path. In this study we generalize this graph cla...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 38 شماره
صفحات -
تاریخ انتشار 1985