TCS Journal 2026 Journal Article
Dirac-type condition for rainbow chorded pancyclicity
- Jie Ma
- Junqing Cai
Suppose H is a collection of graphs H 1, H 2, …, H n + 1, where H 1, H 2, …, H n + 1 are not necessarily distinct, and each Hj has the same vertex set U with | U | = n. A subgraph H with V(H)⊆U is said to be rainbow if no two distinct edges in H originate from the same Hj. The graph collection H is said to be rainbow chorded pancyclic if H admits a rainbow chorded cycle of length l for each l ∈ { 4, 5, …, n }. In this paper, we prove that if δ ( H ) = min { δ ( H j ): j = 1, 2, …, n + 1 } ≥ n 2, then H is rainbow chorded pancyclic, with the following exceptions: (1) n ≥ 4 is even and H 1 = H 2 = ⋯ = H n + 1 ≅ K n 2, n 2; or (2) n = 6 and H 1 = H 2 = ⋯ = H 7 ≅ K 2 □ K 3.