2013/04/22 by João Paulo Costalonga, Costalonga, João Paulo
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1304.6076
arxiv created 2013/04/22 · arxiv updated 2013/04/23
In this paper we prove two main results about obstruction to graph planarity. One is that, if G is a 3-connected graph with a K5-minor and T is a triangle of G, then G has a K5-minor H, such that E(T)\cont E(H). Other is that if G is a 3-connected simple non-planar graph not isomorphic to K5 and e,f∈ E(G), then G has a minor H such that e,f∈ E(H) and, up to isomorphisms, H is one of the four non-isomorphic simple graphs obtained from K3,3 by the addiction of 0, 1 or 2 edges. We generalize this second result to the class of the regular matroids.