Reproduce “Linear-size graphs at every strict dismantling level” on OpenResearch
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About this paper
Jesús F. Espinoza, Martín Eduardo Frías-Armenta, Rosalía G. Hernández-Amador, Héctor A. Hernández-Hernández
The authors construct strict dismantling-level graphs whose sizes grow linearly with the level. Each layer adds a centre whose neighbourhood reproduces the preceding graph, plus two auxiliary vertices; clique-count obstructions rule out competing first deletions. The families have 3k+8 and 4k+4 vertices, giving an upper bound on minimum order, not a general minimality result.
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