A broader perspective on Bondy's theorem for graph connectivity

The concept of bipartite independence number in graph theory has recently been examined in the context of Bondy's pancyclicity theorem. This theorem generalizes the notion of Hamiltonian graphs, stating that if the minimum degree of a graph G is at least its bipartite independence number, then G is Hamiltonian. This result extends the earlier theorem by Dirac, which required the minimum degree to be at least half the order of the graph. The findings by McDiarmid and Yolov have further advanced our understanding of the interplay between connectivity and graph structures.