Finiteness of k-vertex-critical graphs holds in (P4+ℓP1, chair)-free, (P4+ℓP1,P5,bull)-free, (P4+ℓP1,P5,cricket)-free, and more generally (P4+ℓP1,B4(m),B3(m)+)-free graphs, with χ ≤ ℓ+2 for (P4+ℓP1,K3)-free graphs.
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3 Pith papers cite this work. Polarity classification is still indexing.
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Proves if-and-only-if equivalences for toric ring normality and quadratic toric ideal generation between anti-blocking lattice polytopes and their unconditional reflections, plus a graph-theoretic characterization of quadratic symmetric stable set ideals.
Gorenstein simplices with the given h*-polynomial are classified up to unimodular equivalence by strict divisor chains in the divisor lattice of v, yielding an explicit counting formula.
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Vertex-critical graphs in subfamilies of $(P_4+\ell P_1)$-free graphs
Finiteness of k-vertex-critical graphs holds in (P4+ℓP1, chair)-free, (P4+ℓP1,P5,bull)-free, (P4+ℓP1,P5,cricket)-free, and more generally (P4+ℓP1,B4(m),B3(m)+)-free graphs, with χ ≤ ℓ+2 for (P4+ℓP1,K3)-free graphs.
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Algebraic aspects of unconditional lattice polytopes
Proves if-and-only-if equivalences for toric ring normality and quadratic toric ideal generation between anti-blocking lattice polytopes and their unconditional reflections, plus a graph-theoretic characterization of quadratic symmetric stable set ideals.
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Classification and counting of Gorenstein simplices with $h^*$-polynomial $1+t^k+\cdots+t^{(v-1)k}$
Gorenstein simplices with the given h*-polynomial are classified up to unimodular equivalence by strict divisor chains in the divisor lattice of v, yielding an explicit counting formula.