Distribution of Vertices Required a High‐Degree Condition on Partitions of Graphs Under Degree Constraints

ABSTRACT Let be a graph, and let be functions. Let be the union of edges shared by two cycles of order at most four, and let . In this paper, we prove that if for with , and , then can be partitioned into two subgraphs and such that for each . The result is a generalization of some known results and gives a distribution of vertices required by a high‐degree condition on partitions of graphs under degree constraints.