Black-and-white threshold graphs
Combinatorics
2015-03-19 v1 Data Structures and Algorithms
Abstract
Let k be a natural number. We introduce k-threshold graphs. We show that there exists an O(n^3) algorithm for the recognition of k-threshold graphs for each natural number k. k-Threshold graphs are characterized by a finite collection of forbidden induced subgraphs. For the case k=2 we characterize the partitioned 2-threshold graphs by forbidden induced subgraphs. We introduce restricted -, and special 2-threshold graphs. We characterize both classes by forbidden induced subgraphs. The restricted 2-threshold graphs coincide with the switching class of threshold graphs. This provides a decomposition theorem for the switching class of threshold graphs.
Keywords
Cite
@article{arxiv.1104.3917,
title = {Black-and-white threshold graphs},
author = {Ling-Ju Hung and Ton Kloks and Fernando Villaamil},
journal= {arXiv preprint arXiv:1104.3917},
year = {2015}
}