Projective-planar signed graphs and tangled signed graphs

A projective-planar signed graph has no two vertex-disjoint negative circles. We prove that every signed graph with no two vertex-disjoint negative circles and no balancing vertex is obtained by taking a projective-planar signed graph or a copy of −K5 and then taking 1, 2, and 3-sums with balanced signed graphs.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Daniel C. Slilaty
• Keywords: JCT 2007, Projective-planar Signed Graph, Signed Graph, Vertex-disjoint Negative Circles