Two relational structures are indistinguishable by k-RCR if and only if they receive identical homomorphism counts from every structure of generalised hypertreewidth ≤ k.
Lovász Meets Weisfeiler and Leman
4 Pith papers cite this work, alongside 12 external citations. Polarity classification is still indexing.
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Two temporal graphs are order-isomorphic iff they have equal homomorphism counts from all temporal patterns; counting is FPT for bounded toadwidth and dichotomized for total orders.
Additive εn²-approximation for graph edit distance on VC-dimension-d graphs in n^{O(d/ε²)} time, with extensions to quadratic assignment problems and a Weisfeiler-Leman dimension bound for robust graph isomorphism.
Generalizes homomorphism indistinguishability equivalences induced by orthogonal easy quantum groups, including a classification of (0,0)-intertwiners for graph-theoretic versions.
citing papers explorer
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Homomorphism Indistinguishability Beyond Graphs: Relational Weisfeiler--Leman and Hypertree Width
Two relational structures are indistinguishable by k-RCR if and only if they receive identical homomorphism counts from every structure of generalised hypertreewidth ≤ k.
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The Parameterised Complexity of Temporal Motif Counting, and a Lov\'asz-Style Isomorphism Theorem
Two temporal graphs are order-isomorphic iff they have equal homomorphism counts from all temporal patterns; counting is FPT for bounded toadwidth and dichotomized for total orders.
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Robust Graph Isomorphism, Quadratic Assignment and VC Dimension
Additive εn²-approximation for graph edit distance on VC-dimension-d graphs in n^{O(d/ε²)} time, with extensions to quadratic assignment problems and a Weisfeiler-Leman dimension bound for robust graph isomorphism.
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Homomorphism Indistinguishability Relations induced by Quantum Groups
Generalizes homomorphism indistinguishability equivalences induced by orthogonal easy quantum groups, including a classification of (0,0)-intertwiners for graph-theoretic versions.