Date of Original Version
The realization graph G(d)" role="presentation"> of a degree sequence d is the graph whose vertices are labeled realizations of d, where edges join realizations that differ by swapping a single pair of edges. Barrus (2016)  characterized d for which G(d)" role="presentation"> is triangle-free. Here, for any n≥4" role="presentation">, we describe a structure in realizations of d that exactly determines whether G(d)" role="presentation"> has a clique of size n. As a consequence we determine the degree sequences d for which G(d)" role="presentation"> is a complete graph on n vertices.
Discrete Mathematics, vol. 346 (January 2023), no. 1, Article 113184. https://doi.org/10.1016/j.disc.2022.113184
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