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Prime vertex-minors of a prime graph
[article]

2022
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arXiv
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pre-print

A split of a graph is a partition (A,B) of its vertex set such that min{|A|,|B|}≥ 2 and for some A'⊆ A and B'⊆ B, two vertices x∈ A and y∈ B are adjacent if and only if x∈ A' and y∈ B'. A graph is prime if it has no split. A vertex v of a graph is non-essential if at least two of the three kinds of vertex-minor reductions at v result in prime graphs. Allys (1994) proved that every prime graph with at least 5 vertices has a non-essential vertex unless it is locally equivalent to a cycle graph.

arXiv:2202.07877v1
fatcat:wx2tesnwxnhkjdwdlonla3hbku