Title： Bounds and Distribution of Cycle Lengths in Generalized Petersen Graphs

Abstract：Generalized Petersen graphs, denoted by GP(n,k), form an important class of highly symmetric 3-connected cubic graphs. The problem of existence of Hamiltonian cycles in GP(n,k) has been studied for a long time before thoroughly settled. Inspired by Bondy's meta-conjecture that almost every nontrivial condition for Hamiltonicity also implies pancyclicity, we try to figure out the possible lengths of cycles in GP(n,k). We firstly determine the girth of all GP(n,k). For k∈{2,3}, we completely determine all possible cycle lengths in GP(n,k). We also prove that, when k is odd, and n is even and sufficiently large, GP(n,k) is bipartite and weakly even pancyclic.

Speaker：Zhang Zanbo, Professor of Guangdong University of Finance & Economics. His research interests include graph theory and Combinatorics. Many of his results published on《SIAM J. COMPUTING》、《SIAM J. DISCRETE MATH》and《J. GTAPH THEORY》.

Date：2:00pm-3:00pm 2021-8-20（Friday）.

Tencent Meeting ID： 496 941 443

Organizer：School of Mathematical Science

Students and teachers who are interested in graph theory are welcome.