Acyclic Clique-Interval Graphs
نویسنده
چکیده
The class of acyclic clique-interval (ACI) graphs is introduced as the class of those graphs G=(V ,E) whose cliques are intervals (chains) of an acyclic order on the vertex set V . The class of ACI graphs is related to the classes of proper interval graphs, tree-clique graphs and to the class DV (intersection graphs of directed paths of a directed tree). Compatibility between a graph and an acyclic order is de ned, ACI graphs are characterized in terms of it and some special sets of vertices are found by means of the acyclic compatible order. ACI graphs are also characterized in terms of the dual hypergraph of the hypergraph of all cliques of G. Results concerning substitution and reduction preserving the ACI status are established. A strong necessary condition for a graph to be an ACI graph is also given.
منابع مشابه
k - Interval - filament graphs
For a fixed k, an oriented graph is k-transitive if it is acyclic and for every directed path p=u1→u2→...→uk+2 with k+2 vertices, p induces a clique if each of the two subpaths u1→u2→...→uk+1 and u2→...→uk+2 induces a clique. We describe an algorithm to find a maximum weight clique in a k-transitive graph. Consider a hereditary family G of graphs. A graph H(V,E) is called G-k-mixed if its edge ...
متن کاملComputing kernels in graphs with a clique-cutset
In a directed graph, a kernel is a subset of the vertices that is both independent and absorbing. Not all directed graphs have a kernel, and finding classes of graphs having always a kernel or for which deciding the existence of a kernel is polynomial has been the topic of many works in graph theory. We formalize some techniques to build a kernel in a graph with a clique-cutset, knowing kernels...
متن کاملRecognizing edge clique graphs among interval graphs and probe interval graphs
The edge clique graph of a graph H is the one having the edge set of H as vertex set, two vertices being adjacent if and only if the corresponding edges belong to a common complete subgraph of H. We characterize the graph classes {edge clique graphs} ∩ {interval graphs} as well as {edge clique graphs} ∩ {probe interval graphs}, which leads to polynomial time recognition algorithms for them. Thi...
متن کاملClique-width of full bubble model graphs
A bubble model is a 2-dimensional representation of proper interval graphs. We consider proper interval graphs that have bubble models of specific properties. We characterise the maximal such proper interval graphs of bounded clique-width and of bounded linear cliquewidth and the minimal such proper interval graphs whose clique-width and linear cliquewidth exceed the bounds. As a consequence, w...
متن کاملPerfect graphs with polynomially computable kernels
In a directed graph, a kernel is a subset of vertices that is both stable and absorbing. Not all digraphs have a kernel, but a theorem due to Boros and Gurvich guarantees the existence of a kernel in every clique-acyclic orientation of a perfect graph. However, an open question is the complexity status of the computation of a kernel in such a digraph. Our main contribution is to prove new polyn...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999