Signed analogs of bipartite graphs

We characterize the edge-signed graphs in which every 'significant' positive closed walk (or combination of walks) has even length, under seven different criteria for significance, and also those edge-signed graphs whose double covering graph is bipartite. If the property of even length is generalized to positivity in a second edge signing, the characterizations generalize as well. We also characterize the edge-signed graphs with the smallest nontrivial chromatic numbers.

• Type: Journal
• Year: 1998
• Where: DM
• Authors: Thomas Zaslavsky
• Keywords: DM 1998, Double Covering Graph, Edge-signed Graphs, Nontrivial Chromatic Numbers