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Minimal Forbidden Subgraphs for the Klein Bottle with Low Connectivity

SuhkjIn Hur1
1DEPARTMENT OF MATHEMATICS, THE OHIO STATE UNIVERSITY, CoLuMaus, OH 43210

Abstract

Kuratowski proved that a finite graph embeds in the plane if it does not contain a subdivision of either K5 or K3,3, known as Kuratowski subgraphs. Glover posed the question of whether a finite minimal forbidden subgraph for the Klein bottle can be expressed as the union of three Kuratowski subgraphs, such that the union of each pair of these fails to embed in the projective plane. We demonstrate that this holds true for all finite minimal forbidden graphs for the Klein bottle with connectivity <3.