An independent set or stable set of a graph G V, E is a subset S of the Ε½ . vertices set V in which no two are adjacent. Let G be the number of vertices in Ε½ . a stable set of maximum cardinality; G is called the stability number of G. Stability numbers of a graph have been well studied, but little
On maximum internally stable sets of a graph
β Scribed by U. J. Nieminen
- Publisher
- John Wiley and Sons
- Year
- 1974
- Tongue
- English
- Weight
- 270 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0894-069X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let __G__ be a graph on __p__ vertices with __q__ edges and let __r__β=β__q__βββ__p__β=β1. We show that __G__ has at most ${15\over 16} 2^{r}$ cycles. We also show that if __G__ is planar, then __G__ has at most 2^__r__βββ1^β=β__o__(2^__r__βββ1^) cycles. The planar result is best possib
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
## Abstract We determine necessary and sufficient conditions for a complete multipartite graph to admit a set of 1βfactors whose union is the whole graph and, when these conditions are satisfied, we determine the minimum size of such a set. Β© 2008 Wiley Periodicals, Inc. J Graph Theory 58:239β250,
Let G=(V 1 , V 2 ; E ) be a bipartite graph with |V 1 |= |V 2 | =n 2k, where k is a positive integer. Suppose that the minimum degree of G is at least k+1. We show that if n>2k, then G contains k vertex-disjoint cycles. We also show that if n=2k, then G contains k&1 quadrilaterals and a path of orde