Root-to-leaf path random walks on double covers of graded signed graphs normalize the Hodge Laplacian on simplicial complexes and yield Cheeger inequalities for the upper spectrum.
arXiv preprint arXiv:2302.01069 , year=
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Establishes n^{1-ε}-hardness of approximation for dichromatic number and acyclic number on tournaments, plus polynomial-time approximations for ℓ-dicolorable digraphs and special dense cases.
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Root-to-Leaf Path Random Walks, Normalized Hodge Laplacians, and Cheeger Inequalities on Simplicial Complexes
Root-to-leaf path random walks on double covers of graded signed graphs normalize the Hodge Laplacian on simplicial complexes and yield Cheeger inequalities for the upper spectrum.
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Hardness and Approximation for Coloring Digraphs
Establishes n^{1-ε}-hardness of approximation for dichromatic number and acyclic number on tournaments, plus polynomial-time approximations for ℓ-dicolorable digraphs and special dense cases.