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When we have an integer sequence that can be realized as the degree sequence of some graph, we say that the sequence is graphic. While almost any graph theory book describes how a sequence can be tested to see if its graphic, surprisingly (because this testing has common applications), very little has been written about how to do it efficiently. This highlights the gap between simply knowing that a problem is theoretically tractable and being able to implement an efficient algorithm for practical use.
Cloteaux, B.
(2015),
Is This for Real?: Fast Graphicality Testing, Computing in Science & Engineering, [online], https://doi.org/10.1109/MCSE.2015.125
(Accessed June 4, 2023)