## Abstract A cubic triangleβfree graph has a bipartite subgraph with at least 4/5 of the original edges. Examples show that this is a best possible result.
A note on bipartite subgraphs of triangle-free regular graphs
β Scribed by S. C. Locke
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 130 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Lower bounds on the size of a maximum bipartite subgraph of a triangleβfree rβregular graph are presented.
π SIMILAR VOLUMES
## Abstract We show that a maximal triangleβfree graph on __n__ vertices with minimum degree Ξ΄ contains an independent set of 3Ξ΄ β __n__ vertices which have identical neighborhoods. This yields a simple proof that if the binding number of a graph is at least 3/2 then it has a triangle. This was con
We show new lower and upper bounds on the maximum number of maximal induced bipartite subgraphs of graphs with n vertices. We present an infinite family of graphs having 105 n=10 % 1:5926 n ; such subgraphs show an upper bound of O(12 n=4 ) ΒΌ O(1:8613 n ) and give an algorithm that finds all maximal
It can easily be seen that a conjecture of RUNGE does not hold for a class of graphs whose members will be called "almost regular". This conjecture is replaced by a weaker one, and a classification of almost regular graphs is given.