I_{K_{2,2,1}}(e) has at least two local maxima in (0,1) and I_{K_t^-}(e) has a non-global local maximum for t in {5,8,11,...,74}.
Semi-inducibility of 4-vertex graphs
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
For a graph $H$ whose edges are coloured blue or red, the $H$-semi-inducibility problem asks for the maximum, over all graphs $G$ of given order $n$, of the number of injections from the vertex set of $H$ into the vertex set of $G$ that send red (resp. blue) edges of $H$ to edges (resp. non-edges) of $G$. We consider all possible 4-vertex non-complete graphs $H$ and essentially resolve all remaining cases except when $H$ is the 3-edge path coloured blue-blue-red in this order (or is equivalent to this case). Some of our proofs are computer-generated, using the flag algebra method of Razborov.
fields
math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
For every fixed β in [0,1], the extremal S_{2,1}-densities are determined: the upper side completes a four-branch profile via prior work plus new low-density proof, while the lower side is achieved by a one-parameter three-class complement-split family rather than quasi-star/quasi-clique.
citing papers explorer
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Local maximum of inducibility profiles
I_{K_{2,2,1}}(e) has at least two local maxima in (0,1) and I_{K_t^-}(e) has a non-global local maximum for t in {5,8,11,...,74}.
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Fixed-density profiles for the semi-induced 4-vertex star
For every fixed β in [0,1], the extremal S_{2,1}-densities are determined: the upper side completes a four-branch profile via prior work plus new low-density proof, while the lower side is achieved by a one-parameter three-class complement-split family rather than quasi-star/quasi-clique.