Black-and-white threshold graphs

Authors:
Ling-Ju Hung;Ton Kloks;Fernando S. Villaamil
Affiliations:
National Chung Cheng University, Chia-Yi, Taiwan;RWTH Aachen University, Aachen, Germany;RWTH Aachen University, Aachen, Germany
Venue:
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
Year:
2011

Citing 10
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Abstract

Let k be a natural number. We introduce k-threshold graphs. We show that there exists an O(n3) 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.