Venezuela Ap. 47567, Caracas Favaron, O., P. Mago and 0. Ordaz, On the bipartite independence number of a balanced bipartite graph, Discrete Mathematics 121 (1993) 55-63. The bipartite independence number GI aIp of a bipartite graph G is the maximum order of a balanced independent set of G. Let 6 b
Bipartite graphs can have any number of independent sets
β Scribed by V. Linek
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 476 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper we prove that for every positive integer n there exists a bipartite graph with exactly n independent sets.
π SIMILAR VOLUMES
Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,
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
## Abstract A maximal independent set of a graph __G__ is an independent set that is not contained properly in any other independent set of __G__. Let __i(G)__ denote the number of maximal independent sets of __G__. Here, we prove two conjectures, suggested by P. ErdΓΆs, that the maximum number of m
We determine the maximum on n vertices can have, and we a question of Wilf. number of maximal independent sets which a connected graph completely characterize the extremal graphs, thereby answering \* Partially supported by NSF grant number DIMS-8401281. t Partially supported by NSF grant number D S
## Abstract Given a graph __G__ and an integer __k__ββ₯β1, let Ξ±(__G,βk__) denote the number of __k__βindependent partitions of __G__. Let π¦^βs^(__p,q__) (resp., π¦~2~^βs^(__p,q__)) denote the family of connected (resp., 2βconnected) graphs which are obtained from the complete bipartite graph __K~p,q