A graph is well-covered if every maximal independent set is maximum. This concept, introduced by Plummer in 1970 (J. Combin. Theory 8 (1970)), is the focal point of much interest and current research. We consider well-covered 2-degenerate graphs and supply a structural (and polynomial time algorithm
Well covered simplicial, chordal, and circular arc graphs
โ Scribed by Prisner, Erich; Topp, Jerzy; Vestergaard, Preben Dahl
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 427 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
A graph G is called well covered if every two maximal independent sets of G have the same number of vertices. In this paper, we,characterize well covered simplicial, chordal and circular arc graphs.
๐ SIMILAR VOLUMES
The concept of k-coterie is useful for achieving k-mutual exclusion in distributed systems. A graph is said to be well covered if any of its maximal independent sets is also maximum. We first show that a graph G is well covered with independence number k if and only if G represents the incidence rel
Certain fundamental graph problems like recognition, dominating set, Hamiltonian cycle and path, and clique partition, which are hard for well-covered graphs in general, can be solved efficiently for very well covered graphs. We address the question of how far the class of very well covered graphs c
We present a simple optimal algorithm for the problem of finding maximum independent sets of circular-arc graphs. Given an intersection model S of a circular-arc graph G , our algorithm computes a maximum independent set of G in O ( n ) space and O ( n ) or O(n log n ) time, depending on whether the
The class of Z m -well-covered graphs, those in which the cardinality of every maximal independent subset of vertices is congruent to the same number modulo m, contains the well-covered graphs as well as parity graphs. Here we consider such graphs, where there is no small cycle present and obtain a
In this paper, we study the following all-pair shortest path query problem: Given the interval model of an unweighted interval graph of n vertices, build a data structure such that each query on the shortest path (or its length) between any pair of vertices of the graph can be processed efficiently