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Wishlist: Recognize threshold degree sequences #2543

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szhorvat opened this issue Mar 24, 2024 · 0 comments

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szhorvat commented Mar 24, 2024 •

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What is the feature or improvement you would like to see?

A function that recognized threshold degree sequences for various types of graphs (at least both undirected and directed simple graphs).

A threshold degree sequence is a degree sequence with precisely one realization.

Use cases for the feature

Threshold graphs are a well-studied concept in graph theory
Threshold sequences make good test cases for functions dealing with the graph realization problem

References

For undirected graphs this is well studies, see https://en.wikipedia.org/wiki/Threshold_graph
https://www.graphclasses.org/classes/gc_328.html
IGraph/M has this implemented as IGThresholdQ for the undirected case. We can lift the implementation from there.
A treatment for directed graphs is given in https://arxiv.org/abs/1212.1149

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szhorvat added the wishlist label

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