Overfullness of edge‐critical graphs with small minimal core degree
Yan Cao, Guantao Chen, Guangming Jing, Songling Shan · Journal of Graph Theory · 2023
Abstract Let be a simple graph. Let and be the maximum degree and the chromatic index of , respectively. We call overfull if , and critical if for every proper subgraph of . Clearly, if is overfull then . The core of , denoted by , is the subgraph of induced by all its maximum degree vertices. We believe that utilizing the core degree condition could be considered as an approach to attack the overfull conjecture. Along this direction, we in this paper show that for any integer , if is critical with and , then is overfull.