A cycle-space invariant of the <2-distance-graph in the plane


By exhibiting a certain invariant, we prove that the cycle space of the “distance<2” graph in the plane is not generated by the triangles inscribed in unit circles. This solves a problem of Lovász in the negative.

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  1. [1]

    L. Lovász, Research problem,Discrete Mathematics 41 (1982). 111–112.

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Křìž, I. A cycle-space invariant of the <2-distance-graph in the plane. Combinatorica 9, 103–105 (1989). https://doi.org/10.1007/BF02122690

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AMS subject classification (1980)

  • 05 B 40
  • 05 B 45
  • 05 C 38