On Finding the Minimum Bandwidth of Interval Graphs
نویسندگان
چکیده
Let G = (V, E) be an interval graph, with 1 VI = n, and IE] = m. An O(n’ log n) algorithm was proposed in Kratsch (Inform Compui. 74, 14O158 (1987)) to find the bandwidth of G. We show that this algorithm is wrong, and provide a corrected version of the same. Also, it was observed in [4] that the bandwidth of a proper inferual graph can be computed in O(n log n + m) time. We show how this idea can be modified slightly to yield an O(n + m) algorithm.
منابع مشابه
On the bandwidth of Mobius graphs
Bandwidth labelling is a well known research area in graph theory. We provide a new proof that the bandwidth of Mobius ladder is 4, if it is not a $K_{4}$, and investigate the bandwidth of a wider class of Mobius graphs of even strips.
متن کاملChromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs
In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...
متن کاملOn two-dimensional Cayley graphs
A subset W of the vertices of a graph G is a resolving set for G when for each pair of distinct vertices u,v in V (G) there exists w in W such that d(u,w)≠d(v,w). The cardinality of a minimum resolving set for G is the metric dimension of G. This concept has applications in many diverse areas including network discovery, robot navigation, image processing, combinatorial search and optimization....
متن کاملRestrictions of Minimum Spanner Problems
A t-spanner of a graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times their distance in G. Spanners arise in the context of approximating the original graph with a sparse subgraph (Peleg, D., and Scha ffer, A. A. (1989), J. Graph. Theory 13 (1), 99 116). The MINIMUM t-SPANNER problem seeks to find a t-spanner with the minimum number of edges f...
متن کاملBit 34 (1994), 000{000. Finding Minimum Height Elimination Trees for Interval Graphs in Polynomial Time
The elimination tree plays an important role in many aspects of sparse matrix factorization. The height of the elimination tree presents a rough, but usually eeective, measure of the time needed to perform parallel elimination. Finding orderings that produce low elimination trees is therefore important. As the problem of nding minimum height elimination tree orderings is NP-hard, it is interest...
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:
- Inf. Comput.
دوره 95 شماره
صفحات -
تاریخ انتشار 1991