We characterize bipartite Steinhaus graphs in three ways by partitioning them into four classes and we describe the color sets for each of these classes. An interesting recursion ...
Gerard J. Chang, Bhaskar DasGupta, Wayne M. Dym&ag...
We give a proof of Guenin's theorem characterizing weakly bipartite graphs by not having an odd-K5 minor. The proof curtails the technical and case-checking parts of Guenin...
We prove that a triangle-free graph G is a tolerance graph if and only if there exists a set of consecutively ordered stars that partition the edges of G. Since tolerance graphs a...
Whiteley [9] gives a complete characterization of the infinitesimal flexes of complete bipartite frameworks. Our work generalizes a specific infinitesimal flex to include joined gr...
A hierarchy of classes of graphs is proposed which includes hypercubes, acyclic cubical complexes, median graphs, almost median graphs, premedian graphs and partial cubes. Structu...