Three Types of Two-Disjoint-Cycle-Cover Pancyclicity and Their Applications to Cycle Embedding in Locally Twisted Cubes. (18th November 2019) - Kung, Tzu-Liang; Chen, Hon-Chan; Lin, Chia-Hui; Hsu, Lih-Hsing
Abstract: A graph G=(V, E) is two-disjoint-cycle-cover [r_1, r_2] -pancyclic if for any integer l satisfying r_1 ≤ l ≤ r_2, there exist two vertex-disjoint cycles C_1 and C_2 in G such that the lengths of C_1 and C_2 are l and |V(G)| - l, respectively, where |V(G)| denotes the total number of vertices in G . On the basis of this definition, we further propose Ore-type conditions for graphs to be two-disjoint-cycle-cover vertex/edge [r_1, r_2] -pancyclic. In addition, we study cycle embedding in the n -dimensional locally twisted cube LTQ_n under the consideration of two-disjoint-cycle-cover vertex/edge pancyclicity.