trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

A disconnected counterexample to the token-radius conjecture

The graph consisting of one edge and two isolated vertices has Laplacian spectral radius 2, as does its two-token graph, but it is not a star. This refutes the all-graphs statement of Conjecture 1.1 of Song, Dalfo, Fiol and Zhang.

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One edge and two isolated vertices

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A disconnected counterexample to the token-radius conjectureA disconnected counterexampleto the token-radius conjectureThe token-graph cut bound fails on a five-cycle blow-upThe token-graph cut bound failson a five-cycle blow-upNew Laplacian layer maxima decrease on the four-vertex starNew Laplacian layer maximadecrease on the four-vertexstar
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Lean sourceResearch workspace
Status
Closed
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0
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/Graph/TokenGraphLaplacianRadiusRefutation
Repository path
D5/S3/Combinatorics/Graph/TokenGraphLaplacianRadiusRefutation.lean
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sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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