Year: 2026
Type: preprint
Abstract: We investigate rainbow pancyclicity and vertex-pancyclicity of graph systems satisfying a local Ore-type degree condition. All graphs in the system share the same vertex set. We prove that if each graph is 2-connected and satisfies our local Ore condition, then the graph system is either rainbow pancyclic and vertex-pancyclic for cycles of length from 4 to n, or all graphs are identical balanced complete bipartite graphs on an even vertex set. A stronger degree threshold ensures full rainbow vertex-pancyclicity. All thresholds we obtain are tight. Our proofs rely on cycle extension techniques and neighborhood separation arguments.
Source: arXiv (Cornell University)
Authors: Chen, Ailian, Lin, Jiahuang
Institution: Fuzhou University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223054576