Forbidden Induced Subgraphs
Thomas Zaslavsky
TL;DR
This paper surveys various graph classes defined by forbidden induced subgraphs, highlighting differences from other orderings and exploring fundamental questions in graph theory.
Contribution
It provides a comprehensive overview of partial orderings of graphs, focusing on the induced-subgraph ordering and its implications for graph classes like perfect and threshold graphs.
Findings
Comparison of induced-subgraph ordering with other graph orderings
Identification of key graph classes characterized by forbidden induced subgraphs
Discussion of how ordering differences influence fundamental graph questions
Abstract
In descending generality I survey: five partial orderings of graphs, the induced-subgraph ordering, and examples like perfect, threshold, and mock threshold graphs. The emphasis is on how the induced subgraph ordering differs from other popular orderings and leads to different basic questions.
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