On 2K2-free graphs - Structural and Combinatorial View
Abstract
A connected graph is 2K2-free if it does not contain a pair of independent edges as an induced subgraph. In this paper, we present the structural characterization of minimal vertex separator and show that there are polynomial number of minimal vertex separators in 2K2-free graphs. Further, using the enumeration we show that finding minimum connected vertex separator in 2K2-free graphs is polynomial time solvable. We highlight that finding minimum connected vertex separator is NP-complete in Chordality 5 graphs, which is a super graph class of 2K2-free graphs. Other study includes, enumeration of all distinct maximal independent sets and testing 2K2-free graphs. Also, we present an polynomial time algorithm for feedback vertex set problem in the subclass of 2K2-free graphs.
Keywords
Cite
@article{arxiv.1602.03802,
title = {On 2K2-free graphs - Structural and Combinatorial View},
author = {S. Dhanalakshmi and N. Sadagopan and V. Manogna},
journal= {arXiv preprint arXiv:1602.03802},
year = {2016}
}
Comments
15 pages, 5 figures, 4 algorithms, Presented in ICMCE 2015