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DenitionMatchstickgraphGraphGVEsuchthatthereexistsaninjectiveembeddingfVR2withkfv1fv2k21forallfv1v2g2Eandthecorrespondingedgesarenoncrossing DenitionAgraphisrregularifeveryvertex

Denition(Matchstickgraph)GraphG=(V;E)suchthatthereexistsaninjectiveembeddingf:V!R2withkf(v1)f(v2)k2=1forallfv1;v2g2Eandthecorrespondingedgesarenon-crossing. DenitionAgraphisr-regularifeveryvertex

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