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Asymptotic Structure of Graphs with the Minimum Number of Triangles

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arxiv 1204.2846 v2 pith:URS5ZQMX submitted 2012-04-12 math.CO

Oleg Pikhurko , Alexander Razborov This is my paper · ORCID
classification math.CO
keywords asymptoticgraphsnumberstructuretrianglesachievedalgebracharacterizing
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We consider the problem of minimizing the number of triangles in a graph of given order and size and describe the asymptotic structure of extremal graphs. This is achieved by characterizing the set of flag algebra homomorphisms that minimize the triangle density.

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  1. Emergence in graphs with near-extreme constraints

    math.PR 2024-11 conditional novelty 8.0 of 10

    Near the boundary of feasible edge and triangle densities, entropy-optimal graphons are unique, multipodal, and analytic in the constraints, yielding infinitely many phases.

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