Theoretical analysis shows cycles through four vertices and a 2-path in cubic graphs, indicating significant properties in graph theory.
Finding a cycle that contains certain prescribed vertices or edges within a graph is a classical problem in graph theory. It has been established that every [Formula: see text]-connected cubic graph contains a cycle through any nine vertices, which is referred to as the well-known nine-point theorem. In this paper, it is demonstrated that every [Formula: see text]-connected cubic graph contains a cycle through any four prescribed vertices and a [Formula: see text]-path. This result is optimal.
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Li et al. (2025) studied this question.
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