Graphs in which all maximal bipartite subgraphs have the same order [article]

Wayne Goddard, Kirsti Kuenzel, Eileen Melville
2019 arXiv   pre-print
Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite number). We first give examples of them, compare them with well-covered graphs, and characterize those with small or large bipartite number. We then consider graph operations including the union, join, and lexicographic and cartesian products. Thereafter we consider simplicial vertices and 3-colored graphs where every
more » ... ertex is in triangle, and conclude by characterizing the maximal outerplanar graphs that are well-bicovered.
arXiv:1909.07503v1 fatcat:6nx6jawzs5cdjizaa64pfasp2e