Two characterizations of chain partitioned probe graphs
نویسنده
چکیده
Chain graphs are exactly bipartite graphs without induced 2K 2 (a graph with four vertices and two disjoint edges). A graph G = (V, E) with a given independent set S ⊆ V (a set of pairwise non-adjacent vertices) is said to be a chain partitioned probe graph if G can be extended to a chain graph by adding edges between certain vertices in S. In this note we give two characterizations for chain partitioned probe graphs. The first one describes chain partitioned probe graphs by six forbidden subgraphs. The second one characterizes these graphs via a certain " enhanced graph " : G is a chain partitioned probe graph if and only if the enhanced graph G * is a chain graph. This is analogous to a result on interval (respectively, chordal, threshold, trivially perfect) partitioned probe graphs, and gives an O(m 2)-time recognition algorithm for chain partitioned probe graphs.
منابع مشابه
Good characterizations and linear time recognition for 2-probe block graphs
Block graphs are graphs in which every block (biconnected component) is a clique. A graph G = (V,E) is said to be an (unpartitioned) k-probe block graph if there exist k independent sets Ni ⊆ V , 1 ≤ i ≤ k, such that the graph G obtained from G by adding certain edges between vertices inside the sets Ni, 1 ≤ i ≤ k, is a block graph; if the independent sets Ni are given, G is called a partitione...
متن کاملCharacterizing and recognizing probe block graphs
Block graphs are graphs in which every block (biconnected component) is a clique. A graph G = (V,E) is said to be an (unpartitioned) probe block graph if there exists an independent set N ⊆ V and some set E′ ⊆ (N 2 ) such that the graph G′ = (V,E∪E′) is a block graph; if an independent set N is given, G is called a partitioned block graph. In this note we give good characterizations for probe b...
متن کاملABC Editors
Block graphs are graphs in which every block (biconnectedcomponent) is a clique. A graph G = (V,E) is said to be an (unparti-tioned) probe block graph if there exists an independent set N ⊆ V andsome set E′ ⊆ (N2)such that the graph G′ = (V,E∪E′) is a block graph;if an independent set N is given, G is called a partitioned block graph.In this note we give good cha...
متن کاملProbe Ptolemaic Graphs
Given a class of graphs, G, a graph G is a probe graph of G if its vertices can be partitioned into two sets, P (the probes) and N (the nonprobes), where N is an independent set, such that G can be embedded into a graph of G by adding edges between certain nonprobes. In this paper we study the probe graphs of ptolemaic graphs when the partition of vertices is unknown. We present some characteri...
متن کاملProbe interval graphs and probe unit interval graphs on superclasses of cographs
A graph is probe (unit) interval if its vertices can be partitioned into two sets: a set of probe vertices and a set of nonprobe vertices, so that the set of nonprobe vertices is a stable set and it is possible to obtain a (unit) interval graph by adding edges with both endpoints in the set of nonprobe vertices. Probe (unit) interval graphs form a superclass of (unit) interval graphs. Probe int...
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:
- Annals OR
دوره 188 شماره
صفحات -
تاریخ انتشار 2011