Black-and-white threshold graphs
Ling-Ju Hung, Ton Kloks, Fernando Villaamil

TL;DR
This paper introduces k-threshold graphs, provides recognition algorithms, characterizations by forbidden subgraphs, and explores special subclasses, including their relation to switching classes of threshold graphs.
Contribution
The paper defines k-threshold graphs, develops recognition algorithms, and characterizes these graphs and their subclasses via forbidden induced subgraphs.
Findings
Recognition algorithm for k-threshold graphs runs in O(n^3) time.
k-threshold graphs are characterized by a finite set of forbidden induced subgraphs.
Restricted 2-threshold graphs are equivalent to the switching class of threshold graphs.
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.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Graph Labeling and Dimension Problems
